Standing Wave Type Research Articles

Revisiting the difference between traveling-wave and standing-wave thermoacoustic engines - A simple analytical model for the standing-wave one

There are two major categories in a thermoacoustic prime-mover. One is the traveling-wave type and the other is the standing-wave type. A simple analytical model of a standing-wave thermoacoustic prime-mover is proposed at relatively low heat-flux for a stack much shorter than the acoustic wavelength, which approximately describes the Brayton cycle. Numerical simulations of Rott’s equations have revealed that the work flow (acoustic power) increases by increasing of the amplitude of the particle velocity (|U|) for the traveling-wave type and by increasing cosΦ for the standing-wave type, where Φ is the phase difference between the particle velocity and the acoustic pressure. In other words, the standing-wave type is a phase-dominant type while the traveling-wave type is an amplitude-dominant one. The ratio of the absolute value of the traveling-wave component (|U|cosΦ) to that of the standing-wave component (|U|sinΦ) of any thermoacoustic engine roughly equals the ratio of the absolute value of the increasing rate of |U| to that of cosΦ. The different mechanism between the traveling-wave and the standing-wave type is discussed regarding the dependence of the energy efficiency on the acoustic impedance of a stack as well as that on ωτα, where ω is the angular frequency of an acoustic wave and τα is the thermal relaxation time. While the energy efficiency of the traveling-wave type at the optimal ωτα is much higher than that of the standing-wave type, the energy efficiency of the standing-wave type is higher than that of the traveling-wave type at much higher ωτα under a fixed temperature difference between the cold and the hot ends of the stack.

Generation of long waves by an oscillating line source above a flat beach of angle α=π/2M,M∈Z: the 3-d Case

A problem of long-wave generation by an oscillatory line source is discussed in the context of 3-d flow over a plane beach of slope angle α=π/2M,M∈Z extending previous 2-d work by the author with the use of a Kontorovich–Lebedev transform. The placing of the source at a zero of the classical long-wave scattering potential is known to lead to a system of trapped waves and provides a robust check on this generalised theory. The development is based on a solution to a second order source-induced inhomogeneous difference equation and leads to an extension and correction of previous work by Morris (Proc. Camb. Phil. Soc. (1976), 79, 573) where a Green's function (for a reduced problem) was utilised for the case of a beach of unit gradient only. The solution provided in that work was recently deemed incomplete by the author (Appl. Math. Letters, 48, (2015), 135–142) following a parallel investigation on a discrepancy in numerical results from the well-known bench mark models of Peters and Roseau for the classical beach problem. While a full water column response requires a trigonometric factorisation, the complexity of which increases with M⁠, surface response can be more readily calculated using an Abel-summable form of the inverse transform. Full water column analysis is restricted to the simple cases M=2,M=3⁠. It is found, through the asymptotic theory in the transform space that, contrary to Morris' conjecture, there is a resonance at cut-off only for odd values of M and this is verified through computation as wave-number approaches its critical value. Moreover, for cut-off resonance it is found that these amplitudes are directly proportional to the profile of the shortest edge wave possible (in source coordinates) for the chosen value of M⁠. As a result, it therefore follows that cut-off resonance disappears if (for M≥3⁠) the source is placed at a zero of this highest order edge wave. It is also found that the flow regime is generally of standing wave type landward of the source position, an observation which might impact on any subsequent mass transport discussions. An alternative method is also outlined in brief, based on recent work on electromagnetic scattering by a wedge shaped dielectric, here formulated to provide a numerical solution from a singular integral equation but designed to give results valid for arbitrary beach slope. The spectral function thus defined is shown to be consistent with that found in the analytic modelling for the case of unit slope. It remains to establish a robust numerical procedure which will combine appropriately discretised radiation conditions in the spectral space with an efficient means to invert the transform numerically.

Theoretical Study on Standing Wave Thermoacoustic Engine

Applications of thermoacoustic engines are not limited to driving pulse tube cryocoolers. The performance of a thermoacoustic engine is governed by various design parameters like type of resonator, stack geometry, frequency, type of working gas etc. and various operating parameters like heat input, charging pressure etc. It is very important to arrive at an optimum configuration of the engine for which a theoretical model is required. In the present work, a theoretical analysis, based on linear acoustic theory of a standing wave type half wavelength thermoacoustic engine is carried out using DeltaEC software. The system dimensions like length of resonator, stack, hot and cold heat exchangers are fixed with a helium-argon mixture as the working gas and a parallel plate type stack. Later on, two plate spacings, corresponding to helium-argon mixture and nitrogen gas, are used for carrying out analysis with helium, argon, nitrogen, carbon dioxide and helium-argon mixture as working gases of the system. The effect of charging pressure on the performance of the system is studied in terms of resonating frequency, onset temperature, pressure amplitude, acoustic power and efficiency. The conclusions derived from the analysis are reported in the paper.

명량해전 당일 울돌목 조류.조석 재현을 통한 해전 전개 재해석

As a multidisciplinary study encompassing oceanography and history, we have attempted to reanalyze the course of a historical navel battle, Myungryang Naval Battle(September 16th, 1597 according to the lunar calendar) through hindcasting the paleo-tidal currents and -tides(PTC). Firstly, we conducted harmonic analysis using 6-month current data observed at Uldolmok and 1-year elevation data provided by Korea Ocean Research and Development Institute in order to understand their characteristics and to hindcast the PTC. Observation results show that Uldolmok, ~300m wide, relatively narrow channel, is characterized by a flood-dominant mixed mainly semidiurnal tidal regime induced by relatively-strong shallow water constituents, showing closely a standing wave type of tidal current. Further, we hindcasted PTC on the day of Myungryang Naval Battle. Our results were compared and discussed with results(time and speeds of maximum(flood and ebb) currents and high and low water times) of the previous studies estimated from different methods. Lastly, we reconstruct the course of the event of Myungryang Naval Battle recorded in the Admiral Sun-Sin Yi's War Diary(Nangjung Iigi in Korean) based on our hindcasting results.

The self-focusing effect of nondirected acoustic emission in layered media

If an acoustic field from a nondirected pointed source is located in a layered medium, for example, in an aquatic medium, and a halfinfinite space with a bottom, we apply one physical model of the medium or another. Most frequently, the Pekeris waveguide model is used. Two principally different model approaches are possible to solve the boundary prob� lem: the selfconjugate approach (classic) described in (1-3) and the nonselfconjugate approach (general) described in (4). A comparison of these two model solutions was performed in (4), which showed their significant difference in the description of the acoustic field in the boundary layer and near the symmetry axis of the system point source, i.e., the layered medium in the halfspace. In the selfconjugate model formulation, the spec� trum of eigenvalues of the transversal operator corre� sponding to the Pekeris boundary problem is real, which is interpreted as a lack of emission losses in the system waveguide-halfspace. However, imaginary sources appear in the solution, which are distributed along the symmetry axis in the halfspace. These sources, precisely, simulate emission into the half� space at zero power flux through the impedance inter� face waveguide-halfspace. This provides unidirec� tional (phase synchronism) wave motion along the impedance interface and satisfies conditions of local continuity of the field by the pressure and normal component of the oscillation velocity (conditions of ( p, vz) continuity) at the boundary. In the nonselfconjugate model approach, emit� ted waves of the complex spectrum of the transversal operator appear as do the converging response waves, which provide a positive definiteness of the power flux through the impedance interface. However, the total wave motion appears opposite, out of phase, while conditions of ( p, vz)�continuity are satisfied only on average. A real focusing zone formed by converging response waves appears on the symmetry axis as a con� sequence of emitted waves in the total solution. The appearance of converging response waves is explained by the fact that these waves, together with diverging waves, form a field of the standing wave type in the close zone to the emitter and on the symmetry axis, which plays the role of an absolutely rigid boundary where the radial component of the oscillating velocity should turn to zero. The objective of this work is to analyze the acous� tic field focusing effect in the near zone of the emitter immediately at the symmetry axis in a halfspace on the example of the Pekeris model problem and to study its practical application in the investigation of the sea bottom structure using the methods of acous� tic profiling.

Symmetry and bifurcation of periodic solutions in Neumann boundary value problems

We study a vector-valued reaction-diffusion equation with Neumann boundary conditions (u: [0,π] → ℝ^2 ). Unlike what is observed for scalar equations, where no heteroclinic connections involving periodic solutions occur, we find that steady-state/Hopf and Hopf/Hopf mode interactions produce heteroclinic solutions connecting at least one solution of standing wave type. This is achieved by restricting a problem with periodic boundary conditions and equivariant under \mathrm{O}(2) symmetry to a suitable fixed-point space. For completeness, we include a description of the solutions for Hopf bifurcation and mode interactions involving Hopf bifurcation, namely, steady-state/Hopf and Hopf/Hopf.

Standing wave type surface acoustic wave atomizer

A new standing wave type surface acoustic wave (SAW) atomizer is proposed and tested. To investigate atomization characteristics, the earlier progressive wave and the proposed standing wave types of atomizer are compared by means of vibration mode, atomization speed, and electrostatic deposition tests. In the case of the vibration mode and atomization speed tests, the standing wave type showed higher standing wave ratio (SWR) and slower atomization speed than the progressive wave type. In the electrostatic deposition test, a liquid sample is atomized by two types of SAW atomizer combined with two different driving modes, namely continuous and intermittent drive. The deposited dry particles are then measured by field-emission type scanning electron microscopy (FE-SEM) and particle sizes are calculated by image processing software. In the results, only the standing wave with continuous drive showed no second peak within size distribution.

Development of an ultrasmall ‐band linear accelerator guide for a four‐dimensional image‐guided radiotherapy system with a gimbaled x‐ray head

We are developing a four-dimensional image-guided radiotherapy system with a gimbaled x-ray head. It is capable of pursuing irradiation and delivering irradiation precisely with the help of an agile moving x-ray head on the gimbals. Requirements for the accelerator guide were established, system design was developed, and detailed design was conducted. An accelerator guide was manufactured and basic beam performance and leakage radiation from the accelerator guide were evaluated at a low pulse repetition rate. The accelerator guide including the electron gun is 38 cm long and weighs about 10 kg. The length of the accelerating structure is 24.4 cm. The accelerating structure is a standing wave type and is composed of the axial-coupled injector section and the side-coupled acceleration cavity section. The injector section is composed of one prebuncher cavity, one buncher cavity, one side-coupled half cavity, and two axial coupling cavities. The acceleration cavity section is composed of eight side-coupled nose reentrant cavities and eight coupling cavities. The electron gun is a diode-type gun with a cerium hexaboride (CeB6) direct heating cathode. The accelerator guide can be operated without any magnetic focusing device. Output beam current was 75 mA with a transmission efficiency of 58%, and the average energy was 5.24 MeV. Beam energy was distributed from 4.95 to 5.6 MeV. The beam profile, measured 88 mm from the beam output hole on the axis of the accelerator guide, was 0.7 mm X 0.9 mm full width at half maximum (FWHM) width. The beam loading line was 5.925 (MeV)-Ib (mA) X 0.00808 (MeV/mA), where Ib is output beam current. The maximum radiation leakage of the accelerator guide at 100 cm from the axis of the accelerator guide was calculated as 0.33 cGy/min at the rated x-ray output of 500 cGy/min from the measured value. This leakage requires no radiation shielding for the accelerator guide itself per IEC 60601-2-1.

Generalized stability theory of vapor film in subcooled film boiling on a sphere

The previously proposed stability theory of vapor film in subcooled film boiling on a sphere was generalized to take account of interaction between base flow and perturbed components. A disturbance of standing wave type was assumed to be superimposed on the base flows of surrounding liquid and vapor film. For the surrounding liquid, the wave equation was applied to the whole region including the boundary layer and the energy equation was solved analytically by introducing a simplifying assumption. For the vapor film, the basic equations were solved by an integral method. By use of compatibility conditions at the liquid–vapor interface, the solutions for the surrounding liquid and the vapor film were combined to yield an algebraic relation among the vapor film thickness, the order of disturbance and the complex amplification factor of disturbance. The numerical solutions of critical vapor film thickness at which the real part of complex amplification factor was equal to zero were obtained for the disturbances of the zeroth, first and second orders. The numerical results indicated that the vapor film was most unstable for the disturbance of the zeroth order (i.e., uniform disturbance). The calculated value of the critical vapor film thickness for the uniform disturbance compared well with the average vapor film thickness at the minimum-heat-flux point obtained from the immersion cooling experiments of spheres in water at high liquid subcoolings.

2-09-01 A self-running standing wave type ultrasonically levitated linear guide(High power ultrasound)

2-09-01 A self-running standing wave type ultrasonically levitated linear guide(High power ultrasound)

Three-dimensional oscillatory thermocapillary flow in encapsulated liquid bridge

In order to understand the fundamental characteristics of thermocapillary convection in an encapsulated liquid bridge, we conducted a series of unsteady three-dimensional numerical simulations of thermocapillary convection in an encapsulated liquid bridge with either 2 or 3mm inner diameter and 4–7mm outer diameter as well as variable height 1–3 mm heated from the top wall and cooled at the bottom wall with an adiabatic free surface. Simulation conditions correspond to those in the experiments of Majima [S. Majima, Phys. Fluids 13, 1517 (2001)]. The simulation results indicate that thermocapillary convection in an encapsulated liquid bridge is axisymmetric and steady at the small Marangoni number. However, when the Marangoni number exceeds some critical value, the flow will undergo a transition to three-dimensional oscillatory flow, which is characterized by a standing wave type oscillation, i.e., the periodic growth and decay of temperature disturbances from cold disk to heat disk. The critical conditions for the onset oscillatory flow are determined and compared with the experimental results. The details of the flow and temperature fields are discussed, and oscillation frequencies are also exhibited.

Influence of dissolved-air concentration on spatial distribution of bubbles for sonochemistry

The pulsation of ultrasonic cavitation bubbles at various dissolved-air concentration in a sonochemical reaction field of standing-wave type is investigated experimentally by laser-light scattering. When a thin light sheet, finer than half the wavelength of sound, is introduced into the cavitation bubbles at an antinode of sound pressure, the scattered light intensity oscillates. The peak-to-trough light intensity is correlated with the number of bubbles that contribute to the sonochemical reaction. It is shown that as the dissolved air concentration becomes higher, the weighted center of the spatial distribution of the peak-to-trough intensity tends to shift towards the liquid surface. At higher concentration of the dissolved air, a great deal of bubbles with size distribution generated due to coalescence between bubbles disturbs sound propagation to change the sound phase easily. A standing wave to trap tiny oscillating bubbles is established only at the side which is nearer to the liquid surface. Also at higher concentration, liquid flow induced by drag motion of bubbles by the action of radiation force becomes apparent and position-unstable region of bubble is enlarged from the side of sound source towards the liquid surface. Therefore, the position of oscillating bubbles active for sonochemical reaction is limited at the side which is nearer to the liquid surface at higher concentration of the dissolved air.

An Explicit Solution of a Parabolic Equation with Nonlocal Boundary Conditions

We consider a parabolic differential equation with nonlocal boundary conditions. We find an explicit solution of the problem and prove the uniqueness of the solution. Analysis of the explicit solution reveals that it has three physically different linear components. The first component is of standing wave type, and the other two are of right- and left-going wave types, respectively. The speed of propagation of the heat waves depends on constants present in nonlocal boundary conditions. We give examples of right-going heat waves that have constant energy.

Rotational Speed Characteristics of Standing Wave Type Ultrasonic Micro Motors

Causes of rotational speed difference in individual ultrasonic micro motor of standing wave type are experimentally investigated by using five motor sets : rotors, stators and springs. The following results are obtained : (1) The rotational speed difference in each motor is mainly caused by the difference in circumferential speed of projections in each stator. Effects of the difference in each rotor and spring are relatively small. (2) The difference in circumferential speed of projections in each stator is mainly caused by the difference in angle between projection center line and stator nodal line. The smaller angle makes circumferential speed of the projections larger.

Dependence of the characteristics of bubbles on types of sonochemical reactors

Computer simulations of bubble oscillations in liquid water irradiated by an ultrasonic wave have revealed that the characteristic of bubbles depends on types of sonochemical reactors: a horn-type reactor and a standing-wave type reactor. When the acoustic amplitude is large at 20 kHz, the bubble content is mostly water vapor even at the end of the bubble collapse and the temperature inside a bubble at the collapse is relatively low. On the other hand, when the acoustic amplitude is relatively low, the bubble content is mostly noncondensable gas at the end of the bubble collapse and the bubble temperature is relatively high. In a horn-type sonochemical reactor, the former type of bubbles are dominant because many bubbles exist near the horn-tip where the acoustic amplitude is large, while in a standing-wave type reactor the latter type of bubbles are dominant because the Bjerknes force gathers bubbles at a region where acoustic amplitude is relatively low.

Development of a new standing wave type ultrasonic linear motor

We developed a new standing wave type ultrasonic linear motor. The composite stator consists of a metallic plate and two piezoceramic plates bonded to the metallic plate with a spatial phase difference of a half wavelength. The operation principle of the motor was presented with theoretical equations and the feasibility was verified using the finite element method. Experimental fabrication and characterization of a sample motor was performed to confirm the validity of the new structure and the numerical results. The new motor offers identical performance in both forward and backward motions, while maintaining a simple structure and all the characteristic features of an ultrasonic linear motor.

D13 熱音響発振器の基本特性(熱音響エンジン)

Compared with traveling wave thermoacoustic prime mover, standing wave thermoacoustic prime mover has the merit of stability as there is no closed loop in the system. The heat->work conversion efficiency of standing wave type engine is lower than that of traveling wave type theoretically. A standing wave thermoacoustic prime mover has been built to measure its efficiency accurately. Numerical calculations were carried out and the results coincided with experimental results well. Calculations also show that there exists an optimum heat transfer area of stack to get the best efficiency, and also it is true to heat exchangers to improve the efficiency and increase the output power.

Analysis of Linear Viscous Flow with a Free Surface in a Circular Cylinder Subjected to Small-Amplitude Circular Oscillations

A fluid flow with a free surface inside a circular cylinder subjected to horizontal, circular oscillation was analyzed theoretically and numerically under the assumption of small-amplitude oscillation and high Reynolds number. It was shown that the nature of the oscillatory flow is of a standing-wave type when projected onto the axial plane and of a progressive-wave type when projected onto the azimuthal plane. The Stokes drift motion in the azimuthal direction and the steady streaming velocity at the edge of the bottom- and side-wall boundary layers are then used in the numerical computation for the steady axisymmetric recirculatory flow outside the boundary layers. We have found that the solutions can be well predicted by asymptotic analysis for the full Navier–Stokes equations in the low streaming-Reynolds-number limit. A simple experiment on flow visualization revealed a good agreement in the surface flow pattern on the bottom wall. It also provided steady recirculatory flows that were not much different from the numerical results on the whole.

On droplet formation from capillary waves on a vibrating surface

The formation of sprays from a liquid film on a vibrating surface is used by ultrasonic atomizers for applications ranging from humidification to metal–powder manufacturing. The received opinion in the literature is that droplets are formed periodically from the apexes of an orderly pattern of standing capillary waves, with a wavelength that can be related to vibration frequency by stability analysis. It is described how this assumption may be incorrect in that, after droplet formation commences, the orderliness of the standing–wave pattern is lost due to one or more secondary instability phenomena. These phenomena, which lead to disorderliness, are investigated by using high–speed imaging techniques and a low–frequency vibrating film to model the high–frequency case, because of the difficulty of penetrating clouds of small droplets in the latter case. Different modes of droplet formation are identified and the flow patterns responsible for these modes are discussed. Physical mechanisms are proposed from which it is deduced that only a proportion of standing–wave crests can eject droplets, for a given wall–vibration period, and the identity of these ejecting waves should vary from period to period. The model thus developed demonstrates an apparently random ejection of droplets from one wave cell, even though the model itself is deterministic. The disorder of the capillary waves and the occurrence of several droplet–formation routes are sufficient to explain the range of droplet sizes that is produced by ultrasonic atomization.

A standing wave type ultrasonic motor

A standing wave type ultrasonic motor using a piezoelectric ceramic rectangular bar as stator has been successfully developed. Its main performance parameters and applications such as ultrasonic step motor, clock model, and paper feeder etc are reported in this paper.