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tom Vol. 28, no. 2
127-138
EN
General formulae on the heat release caused by any sound in the thermoviscous flow are derived, the well-known limit of the periodic source being traced. Some illustrations based on the claculations on pulse sound and stationary shock wave as acoustic sources are presented.
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A method of separating one-dimensional disturbances into components propagating upwards and downwards and the stationary one in a stratified medium was developed. The system of equations is split into three coupled nonlinear equations of interacting components. Weak nonlinear evolution formulae for the directed and stationary components of a medium with an arbitrary equation of state were obtained. The wave components treated by the numerical calculations keep their propagation direction, even for quite large initial amplitudes. The results of the numerical simulation are presented. The examples demonstrate a nonlinear evolution of the wave propagating downwards for both the models of the atmosphere: the exponentially stratified model and the homogeneous one.
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The study is devoted to standing acoustic waves in one-dimensional planar resonator which containing an ideal gas. A gas is affected by the constant mass force. Two types of physically justified boundary conditions are considered: zero velocity or zero excess pressure at both boundaries. The variety of nodal and antinodal points is determined. The conclusion is that the nodes of pressure and antinodes of velocity do not longer coincide, as well as antinodes of pressure and nodes of velocity. The entropy mode may contribute to the total field in a resonator. It is no longer isobaric, in contrast to the case when the external force is absent. Examples of perturbations inherent to the entropy mode in the volume of a resonator are discussed.
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This study is devoted to the instantaneous acoustic heating of a shear-thinning fluid. Apparent viscosity of a shear-thinning fluid depends on the shear rate. That feature distinguishes it from a viscous Newtonian fluid. The special linear combination of conservation equations in the differential form makes it possible to derive dynamic equations governing both the sound and non-wave entropy mode induced in the field of sound. These equations are valid in a weakly nonlinear flow of a shear- thinning fluid over an unbounded volume. They both are instantaneous, and do not require a periodic sound. An example of a sound waveform with a piecewise constant shear rate is considered as a source of acoustic heating.
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Content available remote Influence of vortices on a progressive quasi-plane acoustic wave
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The projecting of the quasi-plane flow into specific modes yields in a set of coupled equations accounting for all possible interactions of the basic types of motion. A particular case of interaction considers vortices affecting the character of sound propagation. The new dynamic equations describing the propagation of a progressive acoustic beam interacting with a vortex background are derived and discussed. Since two acoustic branches become separated, these equations include the first order derivative with respect to time. It is the main result of the present paper. Illustrations on the scattered acoustic pressure referring to the different types of vortex flow are presented.
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Content available remote Weakly nonlinear dynamics of short acoustic waves in exponentially stratified gas
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The types of linear motion over an ideal gas affected by gravity are specified approximately in the case of large characteristic wave number of perturbation k: k>> 1/H, where H is the scale of density and pressure decrease of the background gas, the so-called height of the uniform gas. The corresponding approximate operators projecting the overall vector of perturbations into specific types are derived, along with equations governing sound in a weakly nonlinear flow. The validity of approximate formulae are verified for the concrete examples of initial waveforms. The numerical analysis reveals a good agreement of these approximate expressions with the exact ones obtained previously by the author. The analysis applies to the weakly nonlinear flow as well, with the small Mach numbers (M<<1). The links inside modes are redetermined by including terms of order M2 and M2/kH.
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Content available Thermal lenses caused by any acoustic source
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EN
The modern theory concerning to the heating cased by powerful sound source is presented. In contrast to the well-known approach allowing to calculate slowly varying heating due to periodic ultrasound, any acoustic sources may be treated. Subtle temporal structure of thermal lens forming may be traced. Formulae governing the forming of the thermal lens by arbitrary (including non-periodic) source are presented. The process is illustrated by some figures.
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tom Vol. 26, no. 2
121-131
EN
Projecting technique is used for a system of coupled nonlinear equations for interacting modes derivation. Three independent modes of the viscous flow: leftwards, rightwards propagating (acoustic) and the stationary one (heat) are specified by a set of orthogonal projectors. The final system of coupled equations is equivalent to the basic one with the accuracy up to the third-order nonlinear terms and its form allows to apply nonsingular perturbations method for an approximate solution in the case when one mode is dominant compared with other iterated modes. Caloric and thermal equations of state are taken in the general form. Thermoviscous media are treated, that leads to a system of coupled equations of the Burgers type. The modified Burgers equation for rightwards mode affected by other ones is obtained as well as its stationary solutions.
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General formulae on small-signal sound velocity and parameter of nonlinearity B=A of a two-component relaxing mixture in the two limiting cases of very low and very high periods of sound (when the thermal equilibrium between components has enough time to establish or not) are derived. Sound parameters are expressed in the terms of partial derivatives of individual equations of state. For the two cases: the mixture of van der Waals gases and the suspension consisting of the ideal gas and tiny solid or liquid inclusions, sound velocity and parameter of nonlinearity B=A are evaluated as functions of mass concentration of one of the parts. The rst example concerns to the mixtures consisting of oxygen and helium, and the second one to the suspension of air and graphite and the water fog. General conclusions about acoustic features of the two-component mixtures under very high and low frequencies are drawn out.
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Nonlinear excitation of slow modes by the planar magnetosonic perturbations in a plasma is discussed. Plasma is an open system due to radiation and external heating. This may stipulate enhancement of wave perturbations and hence the acoustical activity of plasma. Plasma is assumed to be a homogeneous ideal gas with infinite electrical conductivity. The straight magnetic field is orthogonal to the velocity of fluid’s elements. Nonlinear excitation of the non-wave modes (that is, the Alfvén and the entropy modes) by periodic and aperiodic planar magnetoacoustic perturbations, is discussed. The sawtooth wave and the small-magnitude harmonic wave are considered as examples of periodic in time perturbations. The conclusions concern acoustically active and thermally unstable flows as well.
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Nonlinear phenomena of the planar and quasi-planar magnetoacoustic waves are considered. We Focus on deriving of equations which govern nonlinear excitation of the non-wave motions by the intense sound in initially static gaseous plasma. The plasma is treated as an ideal gas with finite electrical conductivity permeated by a magnetic field orthogonal to the trajectories of gas particles. This introduces dispersion of a flow. Magnetoacoustic heating and streaming in the field of periodic and aperiodic magnetoacoustic perturbations are discussed, as well as generation of the magnetic perturbations by sound. Two cases, corresponding to magnetosound perturbations of low and high frequencies, are considered in detail.
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Variations in the thermodynamic state of a dispersive medium, caused by sound, are studied. A bubbly liquid and a Maxwell fluid are considered as examples. Curves in the plane of thermodynamic states are plotted. They are in fact pictorial images of linear relations of excess pressure and excess density in the acoustic wave which reflect irreversible attenuation of the sound energy. The curves account for the nonlinear generation of the entropy mode in the field of sound. In the case of Maxwell fluids, loops may form under some conditions. Curves and loops for some kinds of stationary waveforms and impulse sound are discussed and compared.
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Dynamics of a weakly nonlinear and weakly dispersive flow of a gas where molecular vibrational relaxation takes place is studied. Variations in the vibrational energy in the field of intense sound is considered. These variations are caused by a nonlinear transfer of the acoustic energy into energy of vibrational degrees of freedom in a relaxing gas. The final dynamic equation which describes this is instantaneous, it includes a quadratic nonlinear acoustic source reflecting the nonlinear character of interaction of high-frequency acoustic and non-acoustic motions in a gas. All types of sound, periodic or aperiodic, may serve as an acoustic source. Some conclusions about temporal behavior of the vibrational mode caused by periodic and aperiodic sounds are made.
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The distribution of perturbations of pressure and velocity in a rectangular resonator is considered. A resonator contains a gas where thermodynamic processes take place, such as exothermic chemical reaction or excitation of vibrational degrees of a molecule’s freedom. These processes make the gas acoustically active under some conditions. We conclude that the incident and reflected compounds of a sound beam do not interact in the leading order in the case of the periodic sound with zero mean pressure including waveforms with discontinuities. The acoustic field before and after forming of discontinuities is described. The acoustic heating or cooling in a resonator is discussed.
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The nonlinear dynamics of perturbations, quickly varying in space, with comparatively large characteristic wavenumbers k: k > 1/H, is considered. H is the scale of density and pressure reduction in unperturbed gas, as the coordinate increases (H is the so-called height of the uniform equilibrium gas). Coupling nonlinear equations which govern the sound and the entropy mode in a weakly nonlinear flow are derived. They describe the dynamics of the gas in the leading order, with an accuracy up to the terms k(H)-1. In the field of the dominative sound mode, other induced modes contain parts which propagate approximately with their own linear speeds and the speed of the dominative mode. The scheme of successive approximations of nonlinear links between perturbations in the progressive mode is established. The numerical calculations for some kinds of impulses confirm the theory.
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Content available remote Acoustic streaming caused by modulated sound and wave packets
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The practical applications of sound relate to approximately periodic sounds. It is shown, that theoretical results of acoustic streaming based on a periodic everywhere sound, should be revised in spite of the experimental data demonstrating the essentially different velocities of streaming. A new approach, which allows evaluating the streaming caused by sound of every type, both periodic and non-periodic, leads to similar results. The results of numerical calculations of streaming caused by modulated sound and series of pulses are compared with those given by formulae for a periodic everywhere sound.
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Acoustic properties of a binary mixture consisting of a liquid being in phase equilibrium with its vapor and a ternary mixture including a binary one and a neutral gas are considered. Detailed calculations of the excess entropy of a ternary mixture in terms of its excess pressure and density are carried out with accuracy up to quadratic nonlinear terms. That allows to estimate the small signal sound velocity and the parameter of nonlinearity B/A of the mixture as a whole. The only assumption is that the vapor and the neutral gas are ideal gases. As an example, the ternary mixture consisting of air and water being in equilibrium with its vapor is considered. Two different kinds of ternary mixtures are considered, one associated with the mixture in which the vapor and air occupy a mutual volume, and another associated with a mixture in which the gases occupy the separate volumes.
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Thermal self-action of an acoustic beam with one discontinuity or several shock fronts is studied in a Newtonian fluid. The stationary self-action of a single sawtooth wave with discontinuity (or some integer number of these waves), symmetric or asymmetric, is considered in the cases of self-focusing and self-defocusing media. The results are compared with the non-stationary thermal self-action of the periodic sound. Thermal self-action of a single shock wave which propagates with the various speeds is considered.
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Content available remote Modelling of acoustic heating induced by different types of sound
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Dynamic equation governing acoustic heating is derived by splitting of the conservation laws into acoustic and non-acoustic parts. Numerical simulations result in the general conclusions about efficiency of acoustic heating produced by pulses of different polarity and shape. Efficiency of heating induced by stochastic and regular periodic sound of the identical intensity is numerically investigated.
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Content available Unusual streaming in chemically reacting gases
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2011
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tom Vol. 14
189-198
EN
Nonlinear stimulation of the vorticity mode caused by losses in the momentum of sound in a chemically reacting gas, is considered. The instantaneous dynamic equation which describes the nonlinear generation of the vorticity mode, is derived. It includes a quadratic nonlinear acoustic source. Both periodic and aperiodic sound may be considered as the origin of the vorticity flow. In the non-equilibrium regime of a chemical reaction, sound and its nonlinear effects behave unusual. There may exist vortices whose direction of rotation is opposite to that of the vortices in the standard thermoviscous flows. This is illustrated by example relating to periodic sound. The theory and examples consider cases of both equilibrium and non-equilibrium regime of a chemical reaction.
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