Rayleigh Angle Research Articles

Numerical studies on laminar natural convection inside inclined cylinders of unity aspect ratio

The effect of cylinder inclination on thermal buoyancy induced flows and internal natural convective heat transfer is explored using CFD simulations. The cylinder’s top and bottom surfaces were maintained at different temperatures while the curved surface was adiabatic. The aspect ratio (length/diameter) of the cylinder was unity and the Prandtl number of the fluid was fixed at 0.71. The Rayleigh number of the confined fluid was varied from 10 3 to 3.1 × 10 4 by changing the specified end wall temperatures. The critical Rayleigh number was estimated to be 3800 for the vertical cylinder. Relaxing the convergence criterion caused false hysteresis in the converged results for the vertical cylinder. Typical natural convective fluid flow and temperature patterns obtained under laminar flow conditions are illustrated for various inclinations ranging from 0° to 180°. Flow visualization studies revealed complex three-dimensional patterns. Different thermal–hydrodynamic regimes were identified and were classified in terms of Rayleigh number and angle of inclination. Empirical correlations for the Nusselt number and maximum velocities in the domain as a function of the inclination angle and Rayleigh number are developed.

Numerical prediction of natural convection in vented cavities using restricted domain approach

The present study reports the numerical simulation of natural convection heat transfer from an open square cavity with two side vents provided symmetrically on the side walls. The top wall which is maintained at a constant temperature ( T w), is the heat source for the cavity and the side walls are adiabatic. A restricted domain approach that predicts the regions of inflow, outflow and velocity distributions is employed. The applicability of two types of pressure boundary conditions at entry and exit regions are studied and compared. Non-linear coupled partial differential equations governing natural convection are solved on a structured non-uniform staggered grid using a second-order accurate upwind least square scheme for discretising the convection terms, central difference scheme for diffusion terms and SIMPLER algorithm for pressure–velocity decoupling. An in-house code is developed and is validated with the results of three classical natural convection problems. Simulations have been carried out for a wide range of thermal parameter, Rayleigh numbers (10 4 ⩽ Ra ⩽ 10 8), orientation of the cavity about horizontal (0 ⩽ δ ⩽ 180) and geometrical parameter, vent ratio ( 0.05 ⩽ D L ⩽ 0.25 ) . The numerical simulation predicts the dimensionless mass flow rate through the cavity and variation of local Nusselt number over the hot wall. A correlation for average Nusselt number is developed in terms of Rayleigh number and angle of tilt of the cavity for D L ⩾ 0.1 .

Study by means of liquid side acoustic barrier of the influence of leaky Rayleigh waves on bounded beam reflection

The Schoch effect in ultrasonics, when sound is incident at the Rayleigh angle on a liquid-solid interface, consists of a forward beam displacement of the reflected beam, usually accompanied by a null strip in between the specular portion and the nonspecular reflected beam portion. It is a widely accepted idea that the effect is caused by reflected sound in combination with a sound field emitted by leaky Rayleigh waves. The current work presents an experimental technique to separate and investigate both fields separately by applying an acoustic barrier. The experiments are based on acousto-optic Schlieren photography.

Interfacial destabilization and atomization driven by surface acoustic waves

Surface acoustic wave atomization is a rapid means for generating micron and submicron aerosol droplets. Little, however, is understood about the mechanisms by which these droplets form due to the complex hydrodynamic processes that occur across widely varying length and time scales. Through experiments, scaling theory, and simple numerical modeling, we elucidate the interfacial destabilization mechanisms that lead to droplet formation. Using a millimeter-order fluid drop exposed to surface acoustic waves as it sits atop a single-crystal lithium niobate piezoelectric substrate, large aerosol droplets on the length scale of the parent drop dimension are ejected through a whipping and pinch-off phenomenon, which occurs at the asymmetrically formed crest of the drop due to leakage of acoustic radiation at the Rayleigh angle. Smaller micron order droplets, on the other hand, are formed due to the axisymmetric breakup of cylindrical liquid jets that are ejected as a consequence of interfacial destabilization. The 10μm droplet dimension correlates with the jet radius and the instability wavelength, both determined from a simple scaling argument involving a viscous-capillary dominant force balance. The results are further supported by numerical solution of the evolution equation governing the interfacial profile of a sessile drop along which an acoustic pressure wave is imposed. Viscous and capillary forces dominate in the bulk of the parent drop, but inertia is dominant in the ejected jets and within a thin boundary layer adjacent to the substrate where surface and interfacial accelerations are large. With the specific exception of parent drops that spread into thin films with thicknesses on the order of the boundary layer dimension prior to atomization, the free surface of the drop is always observed to vibrate at the capillary-viscous resonance frequency—even if the exciting frequency of the surface acoustic wave is several orders of magnitude larger—contrary to common assumptions used in deriving subharmonic models resulting in a Mathieu equation for the capillary wave motion, which has commonly led to erroneous predictions of the droplet size.

EVALUATION OF SUB-SURFACE MATERIAL PROPERTIES USING MINIMUM REFLECTION PROFILES METHOD

Backscattered Rayleigh waves from the surface and/or sub-surface of specimens can be changed by scatterers such as micro-cracks, grain boundaries and surface roughness as well as by variations in material properties. In fact, rough surface generates higher energy of backscattered Rayleigh wave than smooth one. So, it is strongly needed to have a quantitative method to evaluate the variation of material properties only. To address such a need, we propose a new method, named as "minimum reflection profile" which measures energy variation of reflected waves from the surface of specimens as changing the angle of incident wave from normal to beyond Rayleigh angle in a pitch-catch immersion setup. Because of minimum reflection profile is less sensitive to roughness of surface than backward radiation profile. Also, we explore performance of the minimum reflection profiles by evaluating the sub-surface material properties of well known materials with various material properties.

Nonlinear Sound Field by Interdigital Transducers in Water

Nonlinear ultrasound beams in water radiated by a surface acoustic wave (SAW) device are examined experimentally and theoretically. SAWs on an 128° X-cut Y-propagation LiNbO3 substrate are excited by 50 pairs of interdigital transducers (IDTs). The device with a 2 ×10 mm2 rectangular aperture and a center frequency of 20 MHz radiate two ultrasound beams in the direction of the Rayleigh angle determined by the propagation speed of the SAW on the device and of the longitudinal wave in water. The Rayleigh angle becomes 22° in the present experimental situation. The fundamental and second harmonic sound pressures are respectively measured along and across the beam using a miniature hydrophone whose active element 0.4 mm in diameter and whose frequency response is calibrated up to 40 MHz. The Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation is utilized to theoretically predict sound pressure amplitudes. The theoretical predictions of both the fundamental and second harmonic pressures agree well with the measured sound pressures.

Deposition of Thin Film Using a Surface Acoustic Wave Device

When a Rayleigh surface acoustic wave (SAW) propagates at a liquid/solid interface, it radiates its energy into the adjacent liquid. If a liquid droplet is loaded on the SAW propagation surface, droplet vibration, streaming, jetting, and atomization are observed. These phenomena are called SAW streaming. In this paper, a novel thin-film deposition method based on the atomization of SAW streaming phenomena is proposed. The liquid with film material is loaded on the SAW propagation surface and the liquid is atomized. The atomization direction depends on the Rayleigh angle, which is determined by the sound velocity in the liquid and the SAW velocity. For easy fabrication of a thin uniform film, the atomization direction is controlled in the perpendicular direction. Using the developed system, the deposition of pigments in ink is carried out. The results observed by scanning electron microscopy (SEM) and atomic force microscopy (AFM) indicate that a pigment layer is formed on a glass plate.

Nonlinear ultrasound beams and Eckart streaming using interdigital transducers

The Inter‐digital transducer (IDT) of X‐Y LiNbO3 128 deg substrate has a rectangular aperture 10 mm×2 mm, and has a center frequency of 20 MHz. The transducer radiates ultrasound beams in two different directions at the Rayleigh angle, that is determined by the propagation speeds of the surface wave on the substrate, and of the longitudinal wave in water, the angle being ±22 deg to the plane normal to the aperture and containing the IDT center electrode. The fundamental and second harmonic sound pressure levels are measured along and across the beam, using a hydrophone whose active element is 0.4 mm in diam and whose frequency response is calibrated up to 40 MHz. The KZK equation is utilized to predict theoretically sound pressure amplitudes [T. Kamakura et al., Acustica 80, 332–333 (1994)]. Especially, the fundamental pressure curves are compared with the Rayleigh integral formula. It has been found that the KZK equation is almost useful. The Eckart streaming in the ultrasound beam is also observed using PIV.

Effect of the surface free energy on the behaviour of surface and guided waves

The aim of this paper is to evaluate the influence of the surface free energy upon the propagation of the eigenmodes of structures, by studying successively (a) the Rayleigh wave for an elastic half-space, (b) the Lamb waves for an elastic layer, and (c) the guided modes for a tri-layer structure (e.g., metal/adhesive/metal). The surface free energy is a parameter which appears in the jump conditions of stresses and displacements at each interface, and which consequently modifies the eigenmodes, solutions of the boundary conditions system. As expected, the Rayleigh wave is dispersive and its velocity increases when the surface free energy increases. In the same way, the velocity of Lamb waves also increases except at normal angle of propagation where the surface free energy does not arise. Moreover, near the Rayleigh angle, the behaviour of the A0 and S0 Lamb modes varies strongly according to the surface free energy. Similar results are observed for the tri-layer structure.

Fast beating null strip during the reflection of pulsed Gaussian beams incident at the Rayleigh angle

It is well known that harmonic bounded Gaussian beams undergo a transformation into two bounded beams upon reflection on a solid immersed in a liquid. The effect is known as the Schoch effect and can be found at the Rayleigh angle for thick plates and at the different Lamb angles for thin plates. Here, a study is made on the effect of pulsed Gaussian beams reflected on solids. It is found experimentally that the Rayleigh wave phenomenon still generates two reflected bounded beams, whereas Lamb wave phenomena do not generate this effect. This fact may be explained intuitively by realizing that the Rayleigh phenomenon is a coincidental phenomenon that is generated in situ, whereas the Lamb wave phenomenon is a non-coincidental phenomenon that is generated only after incident sound is influenced by both sides of a thin plate. Another explanation is the fact that Rayleigh waves are not dispersive, whereas stimulation and propagation of Lamb waves is frequency dependent. A pulse contains many frequencies and therefore only a fraction of the incident pulse is transformed into a Lamb wave. In this paper, numerical simulations are performed that show that actually the Schoch effect does occur neither for Rayleigh waves, nor for Lamb waves. As a matter of fact, a pulse, incident at the Rayleigh angle, generates two reflected lobes with a null zone of a different kind. The null zone is beating several times during the passage of each pulse. This results in a ‘null zone’ having a lower mean intensity than any of the two lobes, still less outspoken than for the case of harmonic incident bounded beams. This effect does only occur for Rayleigh wave generation and is much less outspoken for Lamb wave generation.

Fringed sound fields and their interaction with liquid–solid interfaces

On the one hand, it is well known that Gaussian beams posses the ability to stimulate Rayleigh waves, resulting in the Schoch effect, a lateral beam displacement. This effect, often characterized by a reflected sound pattern consisting of two anti-phase beams, is due to the re-radiation of sound because of the stimulation of leaky Rayleigh waves. On the other hand, fringed sound beams are characterized by the fact that they consist of a number of neighboring anti-phase narrow beams. They are a first approximation of a sound field originating from a phased array of harmonic vibrating crystals in which each crystal vibrates in anti-phase compared to its neighbor. The individual lobes within the fringed sound pattern diverge much less than standard Gaussian beams of the same size. The current study investigates the interaction of fringed beams with a liquid–solid interface. It is found that under certain conditions, a fringed beam, incident at the Rayleigh angle, produces a reflected sound pattern that contains a wide lobe that is not fringed. It is also shown that under other conditions, contrary to the famous forward displacement of the reflected sound for incident Gaussian beams, a strong backward displacement occurs for fringed beams.

Rayleigh-wave diffraction in ultrasonic testing of chemical plant

Experimental results are described that serve to improve methods of ultrasonic monitoring for engineering components. Observed relationships are obtained for the reflection coefficient R and transmission coefficient D and for the sum R2 + D2 as a function of the depth of extended crack models for ultrasonic piezoelectric detectors with Rayleigh angles for the prism under various irradiation conditions.

Reflection and time-reversal of ultrasonic waves in the vicinity of the Rayleigh angle at a fluid-solid interface

When sending a plane ultrasonic wave toward a fluid-solid interface, the reflected wave is affected, depending on the incident angle. Around the Rayleigh angle the reflection coefficient has a strong and rapidly varying imaginary part. This has the effect of distorting the reflected wave front. If this reflected wave is time-reversed and sent back toward the interface, the reflected wave of this time-reversed wave should not present any distortion, as the time-reversal process restores the original phases. A theoretical and experimental study of these phenomena has been done. The distortion of the reflected waves around the Rayleigh angle is observed and as expected this distortion is canceled by the time-reversal process. However a significant loss of energy in the time-reversed signal is observed for incident angles around the Rayleigh angle, as part of the energy contained in the Rayleigh wave escapes the time-reversal mirror and is lost for the time-reversal process. In a second part, it is shown by simulations and experiments how this signal distortion by reflection around Rayleigh angle influences spatial focusing of waves by time-reversal or simple time-delay methods.

Non Destructive Tests of Structural Bonds by Guided Ultrasonic Waves: Effect of a Surface Pretreatment or a Localized Defect

The aim of this study was to propose a non destructive method to test the mechanical quality of a bond aluminium/epoxy/aluminium. Thus, for each aluminium/epoxy interface, an intermediate interface modelling between a simple geometrical interface and an interphase (3D material medium), i.e. a 2D material medium. In order to describe the surface stresses, we introduce the surface free energy (the surface tension). This parameter appears in the jump conditions of stresses and displacements at each aluminium/epoxy interface. So, it influences the ultrasonic waves propagation and particularly the guided modes of the tri-layer structure. The results show that the surface free energy does not arise at normal angle of propagation, whereas near the Rayleigh angle, the behaviour of the A0 and S0 Lamb modes varies strongly according to its value. Such a modelling seems well adapted to take into account the pre-treatments of the aluminium plates or some localized interface defects.

Study of the scattering of leaky Rayleigh waves at the extremity of a fluid-loaded thick plate

A study by means of the Schlieren technique for the visualization of the ultrasonic beams has revealed that when the leaky Rayleigh waves propagating along the horizontal edge of a thick fluid-loaded solid plate are scattered at the extremity of the plate, they travel around the corner and start leaking into the liquid along the Rayleigh angle measured from the normal to the vertical edge of the plate. Furthermore, the study reveals that the leaky Rayleigh waves are stimulated by the border of an incident ultrasonic-bounded beam more than by the interior of the beam. A comparison with an earlier work shows that the characteristics of the scattering of the leaky Rayleigh waves at the edge of the plate is very different from that of the Scholte–Stoneley waves.

Generalized Snell’s law and its possible relation to coherent backscattering of ultrasonic waves

The cause of backscattering in the Rayleigh angle has first been explained by means of finite beam models in which there are inherently present backward traveling components that explain the backscattering effect. Later, the nature of backscattered sound was proved to consist mostly of incoherent sound due to material anomalies. The present work shows that besides the well known real Snell’s law: i.e., continuity of the frequency and continuity of the wave vector component along the interface, there is also the possibility of a complex solution of Snell’s condition of continuity. The latter shows that it is possible that a part of the incident sound gets reflected into nonspecular directions including the backscatter direction. Furthermore, it is shown that this sound must have a different frequency than the incident frequency.

The reflection of bounded inhomogeneous waves on a liquid/solid interface.

Fourier analysis and normal mode theory are used to describe the reflection of bounded inhomogeneous waves on a liquid/solid interface. Nonspecular reflection phenomena in the Rayleigh angle are studied in detail. In this way, an explanation is given for the Rayleigh dip phenomenon for positive inhomogeneity factors and the related result of a reflection coefficient larger than unity when the sign of the inhomogeneity factor is reversed. In the limit of large beamwidths, the reflection coefficient predicted by the infinite plane inhomogeneous wave theory is obtained. These results are entirely consistent with the experimental work published by Deschamps [J. Acoust. Soc. Am. 96, 2841-2848 (1994)]. The energy efficiency of Rayleigh wave excitation is investigated as well. It is shown that for large beamwidths, the energy efficiency for bounded inhomogeneous waves is considerably higher in comparison with Gaussian and square-profiled beams.

Circumferential resonance modes of solid elastic cylinders excited by obliquely incident acoustic waves.

When an immersed solid elastic cylinder is insonified by an obliquely incident plane acoustic wave, some of the resonance modes of the cylinder are excited. These modes are directly related to the incidence angle of the insonifying wave. In this paper, the circumferential resonance modes of such immersed elastic cylinders are studied over a large range of incidence angles and frequencies and physical explanations are presented for singular features of the frequency-incidence angle plots. These features include the pairing of one axially guided mode with each transverse whispering gallery mode, the appearance of an anomalous pseudo-Rayleigh in the cylinder at incidence angles greater than the Rayleigh angle, and distortional effects of the longitudinal whispering gallery modes on the entire resonance spectrum of the cylinder. The physical explanations are derived from Resonance Scattering Theory (RST), which is employed to determine the interior displacement field of the cylinder and its dependence on insonification angle.

Unified theory for parallel and focused beam nonspecular reflection at liquid-solid interfaces

This paper presents a theoretical model based on wave mechanics for the reflection of focused and parallel ultrasonic beams from a liquid-solid interface. The incident beam is defined by a Gaussian velocity distribution along a plane emitter, and the reflected beam is described through its pressure field by means of asymptotic analysis based on the short wave hypothesis. In the case of a focused reflected beam, nonspecular phenomena are observed for any angle of incidence. However, in the case of a parallel reflected beam, nonspecular reflection only occurs if the incidence of the beam is in the neighborhood of the Rayleigh angle. The objective of this paper is to discuss in detail the physical mechanisms of nonspecular reflection for both focused and unfocused beams and to provide an understanding of the complex phenomena related to nonspecular reflection of ultrasonic beams, which plays an important role in scanning acustic microscopy for materials nondestructive characterization.

Experimental study on the non- specularly reflected ultrasonic beam on a liquid- solid interface

The reflected fields of a slightly divergent ultrasonic beam on a liquid-solid interface are recorded by a Schlieren system, and the lateral beam displacements on the interface are measured. The range of the incident angle θ i is ±5° around the Rayleigh angle θ c . The displacements Δ are found to decrease as the incident angle increases. Theoretical calculation reveals that the displacements decrease with the increase in the incident angle for a divergent incident beam, but increase with that for a convergent one. The calculated curve of Δ - θ i are in agreement with the experimental results.