Nonlinear Standing Waves

The influence of the vibrational action on a cylindrical cavity filled with a viscous perfect gas is studied numerically. The problem is solved in a two-dimensional axisymmetric statement. The cavity walls are thermally insulated. The numerical solution of the problem is compared with the analytic one in the linear approximation. The nonlinear effects and the non-one-dimensional effects are described.

The study of nonlinear sustained oscillations in ducts requires taking into account a variety of relevant physical phenomena, which may occur at different scales, and which therefore are described by different fluid dynamics regimes. In the present work the joint effect of these phenomena is investigated by means of numerical simulation, using a full-wave finite volume method (FiVoNAGI) over a 2D spatial domain assuming axial symmetry, which includes nonlinear propagation and thermoviscous attenuation over a wide range of scales. Excitation at one end of a straight cylindrical tube, open at the other end, is provided by a nonlinear feedback mechanism. First, a transitory state is observed, which is finally followed by a sustained-oscillation state with a self-regulated resonance frequency. For sufficiently large values of the excitation amplitude, shock waves are formed, and their development can be analyzed in terms of progressive waves. The results obtained reproduce qualitatively...

In milli/microchannel, fluid flows are essentially laminar and, as a consequence, heat transfer is limited. An important application of millichannels is mixing of several flows. In this article we present mixing of two fluid flows at two different temperatures with the objective of strongly decreasing the time needed to obtain a mixture at a homogeneous temperature. To increase heat and mass transfer, we propose an active enhancement technique by generating secondary flows by using ultrasonic waves. A mixer has been realized consisting of a millichannel fed by two fluids coupled to a piezoelectric transducer with a vibrating frequency (37.7 kHz) adapted to the channel width. A test bench has been realized to measure mixing properties of the mixer with and without ultrasound for specific equivalent Reynolds number (Re eq ≤ 23). At this frequency, vortices were formed to break the flow laminarity by generating a velocity field with significant transverse components. The observed patterns revealed vortices parallel with the transducer surface corresponding to modal Rayleigh-like streaming. To characterize the mixing performance a thermal mixing criterion (C M) based on input/output temperatures was defined which showed a significant increase in the presence of Rayleigh-like streaming patterns.

The tripartite communion between the sphere, the spiral and the language implies a conceptual leap that clarifies the relations of the form's hierarchical structures as it starts to take shape, from the sphere through the spiral and finally to and into the symbol, a connection systematically exemplified throughout the conceptual narrative endeavour that is simply clarifying in a systematized way, the origin, the essence and the hierarchy of the shape's diversity at the level of the mineral and biological world as well as at the level of the artefact of the human origin, based on the levers of the symbolic thinking. The need to understand the natural cyclicities and harmonic rhythms, from the macrocosmic scale, then found in the biosphere in the chain of trophic cycles, and finally in the animal plant species, where the harmonic rhythm is revealed from the social dynamics, to the individual, system, organ and finally at the intimate level of the dynamics of metabolism and cell division intimately orchestrated by the mysterious score of the genetic code. The laws of harmonic proportions based on recurring strings and positive / negative feedback loops seen as open stationary systems undoubtedly operate throughout this morphodynamic dimensional range.

Acoustic streaming caused by a large amplitude resonant oscillation of an ideal gas in a two-dimensional resonator is numerically studied by solving the system of Navier-Stokes equations with a finite-difference method, without the assumption of symmetry of the flow field. The sound field including shock waves is precisely determined, and then, the streaming velocity field is evaluated in terms of a time-averaged mass flux density vector. We shall demonstrate that, in the case where the amplitude of gas oscillation is moderately large, an asymmetric quasi-steady streaming is established after more than a thousand of oscillations of sound source.

Menentukan cepat rambat gelombang pada dawai C. Dasar Teori : Panjang dawai adalah jarak dari sumber getar atau osilator sampai ke katrol licin, karena hanya pada bagian inilah dawai dirambati gelombang transversal. Tegangan dawai setara dengan gaya berat beban, sedangkan frekuensi gelombang sama dengan frekuensi getaran osilator D. Alat dan Bahan

In milli/microchannel, fluid flows are essentially laminar and, as a consequence, heat transfer is limited. An important application of millichannels is mixing of several flows. In this article we present mixing of two fluid flows at two different temperatures with the objective of strongly decreasing the time needed to obtain a mixture at a homogeneous temperature. To increase heat and mass transfer, we propose an active enhancement technique by generating secondary flows by using ultrasonic waves. A mixer has been realized consisting of a millichannel fed by two fluids coupled to a piezoelectric transducer with a vibrating frequency (37.7 kHz) adapted to the channel width. A test bench has been realized to measure mixing properties of the mixer with and without ultrasound for specific equivalent Reynolds number (⩽ Re 23 eq). At this frequency, vortices were formed to break the flow laminarity by generating a velocity field with significant transverse components. The observed patterns revealed vortices parallel with the transducer surface corresponding to modal Rayleigh-like streaming. To characterize the mixing performance a thermal mixing criterion (C M) based on input/output temperatures was defined which showed a significant increase in the presence of Rayleigh-like streaming patterns.

In this paper, acoustic streaming generated by standing waves in a cylindrical enclosure filled with water is simulated. The effects of geometry, vibrating amplitude and frequency on formation of streaming structures are numerically investigated. The vibrating source is located at the central region of the lower plate. This source generates a plane wave at the bottom of the cylinder. The complete Navier-Stokes equations are considered and an explicit finite-difference method is used to track the acoustic waves. Water in this simulation is assumed to be a Newtonian rotational compressible single-phase liquid with an accurate equation of state. Equations are derived in Lagrangian cylindrical coordinates, using the condition of axial symmetry. The variation of acoustic pressure demonstrates a periodic modulation. The shape of the mean flow field in a period of the modulation does not differ significantly from the second period and there is a steady state condition for all periods. Results showed stronger acoustic streaming because of a decrease in enclosure height and decrease in frequencies.In addition, the increase in the enclosure radius or radius of the vibrating plate and the increase in the maximum displacement of the vibrating plate caused higher acoustic streaming velocities.

Acoustic streaming motion in a compressible gas filled two-dimensional rectangular enclosure is simulated and the effects of the sound field intensity on the formation process of streaming structures are investigated numerically. The oscillatory flow field in the enclosure is created by the vibration of the left wall of the enclosure. The frequency of the wall vibration is chosen such that the lowest acoustic mode propagates along the enclosure. The fully compressible form of the Navier-Stokes equations is considered and an explicit time-marching algorithm is used to track the acoustic waves. The formation of the wave field in the enclosure is computed and fully described and the acoustic boundary layer development is predicted. The interaction of the wave field with viscous effects and the formation of streaming structures are revealed by time-averaging the solutions over a given period. The strength of the pressure waves associated with the acoustic effect and the resulting streaming flow pattern is found to be strongly correlated to the maximum displacement of the wall during a vibration cycle. The wave form determines the shape of the steady streaming structures in the oscillatory flow field.

Convective heat transfer in a differentially heated shallow rectangular enclosure due to the vibration of a vertical side wall is investigated numerically. The frequency of the wall vibration is chosen such that an acoustic standing wave forms in the enclosure. The fully compressible form of the Navier-Stokes equations is considered and an explicit time-marching algorithm is used to explicitly track the acoustic waves. The steady second order flow structures, namely acoustic streaming, are found to be more significant than the primary oscillatory flow field on the cooling rates. The model developed can be used for the analysis of low and temperature fields driven by acoustic transducers. Effects of thermoacoustic wave motion on the developing natural convection process in a compressible gas-filled square enclosure are also investigated numerically. In the cases considered, the left wall temperature is raised rapidly (impulsively or gradually) while the right wall is held at a specified temperature. The strength of the pressure waves associated with the thermoacoustic effect and resulting flow patterns are found to be strongly correlated to the rapidity of the wall heating process.

Acoustic streaming (AS) denotes the effect where a flow in a fluid is driven by the absorption of a sound wave. In order to have a significant effect in practice, the sound wave requires a high frequency (typically order of ultrasound) and high amplitude. In metal processing industry this treatment is applied to obtain grain morphology adjustments during the solidification of metal. Improvement and further development of this technique focus on numerical modeling to reduce substantial costs for test rigs and field tests. This study presents a numerical model which takes into account acoustics and fluid dynamics. An oscillating sonotrode is placed into the fluid, emitting high-amplitude into the fluid. The distribution of the resulting sound field induces a body force described by an additional source term in the momentum balance of the fluid. The results have been experimentally validated with a small-scale laboratory model using water, seed oil and glycerin as sample fluids. By adj...

Propagation of weak shock waves and strongly nonlinear acoustic waves of the lowest order nonplanar mode in a circular duct filled with an ideal gas is numerically investigated by using a high resolution upwind TVD scheme. The results show that, when the nonlinearity is moderately strong and the source frequency is moderately high, the initial sinusoidal wave profile can evolve into shocks, although according to the weakly nonlinear theory a nonlinear Schrödinger equation determines the wave motion in a steady state, where a shock wave does not appear. Furthermore, strongly nonlinear waves can induce a vortex-ring-like streaming jet (mean mass flow), by which the density of the gas in the neighborhood of the vortex core decreases more and more as time goes by. The resulting low-density region is not only of high vorticity but also of high entropy and high temperature.

The large amplitude standing wave excited in a resonator induces acoustic Streaming ofRayleigh type outside the acoustic boundary layer on the wall of the resonato~: For the case that the resonator is a two-dimensional rectangular box, the streaming motion with large Reynolds number is examined numerically. The two-dimensional incompressible Navier-Stokes equations with no external force are used as the governing ~quations for the streaming velocity, which is defined by a tiJDe..averaged mass flux ~nsity vector. The steady velocity component at the outer edge of the acoustic boundary layer, which induces Rayleigh type ~ is employed as the boundary condition for the Navier-Stokes equations. By using a finite-diJference method, we shall show the existence of multiple s~ solutions.

Acoustic streaming is a fundamental nonlinear phenomenon resulting from high frequency vibration in fluids. Known and investigated by Rayleigh and contemporary scientists, it attracts renewed interest due to the availability of powerful computational tools, advanced photography and precise laser velocimetry instrumentation, which can produce accurate experimental results. Its physical mechanism however is still not clearly understood. The analysis appears limited by the traditional premises of harmonic analysis, radiation force and wave propagation and reflection with the focus on nonlinear terms of the inertial frame formulations. Following our earlier analysis of nonlinear effects on rigid particles in a streaming fluid using time domain (TD) finite element (FE) analysis with a moving mesh via Comsol™, we present the modelling of ultrasonic streaming alone. We use state of the art laser velocimetry instrumentation to measure the average velocity of 0.5µm latex tracer particles in a 0.3-4 mms-1 streaming water insonified in the 1MHz frequency range. We use LabView™ virtual instrument to analyse light scattered by a swarm of particles in the moving fringes of crossed laser beams and find the ensemble particle motion from the frequency spectrum of the signal. In order to verify the FE modelling results with respect to the streaming velocity, the electric power is monitored at the transducer terminals. Our FE simulation, based on the Navier-Stokes (NS) equation for viscous incompressible fluids, does not involve wave propagation and radiation but is capable of representing the transient development of streaming, effects of boundaries and effects of the character of the ultrasonic source. Our investigation shows that streaming is neither implied by a time-varying topology nor associated with the asymmetry or even with the movement of the source or the fluid surface. Surprisingly, the streaming velocity is increased by making the enclosure fully symmetrical or by using a 'bodiless' distributed pressure source. Observations reveal not only evolving vortices but a more complex character of streaming than generally shown, including reversed streaming. Animations reveal transient development of a volume of streaming medium progressively 'propagating' away from the source and following a self contained volume of a pressure 'valley' travelling ahead of it and apparently attracting its motion.

Abstrak-Praktikum Hukum Melde pada kali ini bertujuan untuk mengetahui panjang gelombang stasioner, mengetahui hubungan antara cepat rambat gelombang (V) dengan gaya tegangan tali (F) serta menganalisa factor-faktor yang mempengaruhi kecepatan gelombang pada tali. Prisinsip yang digunakan adalah prinsip Hukum Melde pada gelombang transversal dan gelombang stasioner. Percobaan ini dilakukan dengan lima jenis variasi tali, yaitu wol, nilon, bol, polister dan katun. Dalam percobaan ini, sebanyak 3 kali pengulangan telah dilakukan pada masing-masing jenis tali. Terdapat 2 jenis percobaan pada judul ini, percobaan pertama dilakukan untuk mengetahui nilai dari panjang gelombang, sedangkan percobaan kedua dilakukan untuk mengetahui hubungan antara cepat rambat gelombang (v) dengan tegangan tali (F). Terlihat dari grafik data yang didapat bahwa hasil yang diperoleh dari praktikum pada kali ini adalah hubungan antara cepat rambat gelombang (v) dengan gaya tegangan tali (F) adalah berbanding lurus. Dan hubungan antara cepat rambat gelombang (v) dengan massa jenis tali (μ) berbanding terbalik. Faktor-faktor yang memengaruhi cepat rambat gelombang (v) antara lain massa beban, tegangan tali, massa tali, massa jenis tali dan panjang tali.

Abstrak-Dalam kehidupan sehari-hari secara tidak sadar kita sering menerapkan prinsip-prinsip fisika, salah satunya adalah prinsup Hukum Melde yang dapat kita terapkan saat kita melakukan penyetelan senar gitar. Percobaan ini mempelajari tentang Hukum Melde dengan tujuan mengetahui panjang gelombang stasioner, mengetahui hubungan antara cepat rambat gelombang dengan gaya tegangan tali dan menganalisa faktor-faktor yang memengaruhi kecepatan gelombang pada tali. Prinsip yang digunakan dalam percobaan ini adalah Hukum Melde. Pada saat percobaan dilakukan pada tali bol yang memiliki rapatan massa 0,000496 kg/m dengan tegangan tali 0,6589 N; 0,5922 N dan 0,6139 N diperoleh cepat rambat secara berturut-turut 36,44 m/s; 34,55 m/s dan 35,18 m/s. Sedangkan saat percobaan dilakukan pada tali nylon yang memiliki rapatan massa 0,0002585 dengan tegangan tali yang sama, diperoleh cepat rambat secara berturut-turut 50,48 m/s; 47,86 m/s dan 48,73 m/s. Kesimpulan yang didapat dalam percobaan ini adalah faktor-faktor yang memengaruhi cepat rambat gelombang diantaranya adalah massa dan panjang tali (rapatan massa) serta tegangan pada tali tersebut.

The visualisation of sound is one of the ancestral human dreams. Capturing the image of the aural ephemeral has been of great interest for scientific environments to this day. Almost everything in the universe is in a vibration state. Clarifying the hierarchy, the origin and co-substantiality of form with the natural language algorithm, grafted on phenomenal synergies, inextricably situates form as a result of stationary wave interference in conjunction with symbolic language-induced inferences. The influence of acoustic wave fields on liquids reveals surprising morphodynam-ic frames in response to fluid which is crossed by the train of sound waves which induce and maintain stationary waves, imperceptibly shaping the carefully selected liquid. In fact, the universe is reduced to expressing order through sphere, genuine brick of the open, immeasurable, infinite construct, which inhabits the geometry of spheres with morphodynamic, disk or spiral adjacencies. This geometric minimal-ism allows the existence, at the tiny thinness of the biosphere surface, of the entire morphological diversity, subject to a permanent construction and deconstruction. The visualisation of sound is one of the ancestral human dreams. Capturing the image of the aural ephemeral has been of great interest for scientific environments to this day. Almost everything in the universe is in a vibration state. Clarifying the hierarchy, the origin and co-substantiality of form with the natural language algorithm, grafted on phenomenal synergies, inextricably situates form as a result of stationary wave interference in conjunction with symbolic language-induced inferences. Standing waves obtained through acoustic stimulation over the liquids or smoothly divided powder uncover a vast territory of phenomenological research, calling for an exciting approach based on the dynamic of fluids, involving the laminar flowing but also the turbulent, cycloid flowing currents that create levo-dextrorotatory vortexes. Thus, observing and classifying these rhythmic phenomena, raises interest specifically in situating them between the turbulent asymmetry and polygonal symmetry. The illustrious Michael Faraday dedicates a study to the relation between sound and mor-phodynamic phenomena found at the surface of the viscous fluids, naming the wavy surface presenting crests and valleys fluid crispation, later becoming Faraday crispation. Of course the standing waves are characterised by being generated in finite spaces, either circular, square or another geometric shape, a fact which obviously modifies the stationary dynamic, as well as the morphology of the wave surface.

Abstrak—Percobaan Melde bertujuan untuk mengetahui panjang gelombang stasioner, mengetahui hubungan antara cepat rambat gelombang (v) dengan gaya tegangan tali (F), menganalisis faktor – faktor yang mempengaruhi kecepatan gelombang pada tali. Prinsip yang digunakan pada percobaan ini adalah menggunakan kaidah gelombang transversal dan gelombang stasioner. Percobaan ini dilakukan dengan tiga variasi tali, yaitu nilon, bol, dan woll, dan lima kali pengulangan pada masing-masing jenis tali. Dimana percobaan pertama dilakukan untuk mengetahui nilai dari panjang gelombang. Sedangkan percobaan kedua dilakukan untuk mengetahui hubungan antara cepat rambat gelombang (v) dengan tegangan tali (F). Sehingga, dapat diketahui hubungan antara cepat rambat dengan gaya tegangan tali (F) adalah berbanding lurus. Faktor-faktor yang memengaruhi cepat rambat gelombang (v) antara lain massa beban, tegangan tali, massa tali, massa jenis tali, dan panjang tali.

The study of nonlinear frequency mixing for acoustic standing waves in a resonator cavity is presented. Two high frequencies are mixed in a highly nonlinear bubbly liquid filled cavity that is resonant at the difference frequency. The analysis is carried out through numerical experiments, and both linear and nonlinear regimes are compared. The results show highly efficient generation of the difference frequency at high excitation amplitude. The large acoustic nonlinearity of the bubbly liquid that is responsible for the strong difference-frequency resonance also induces significant enhancement of the parametric frequency mixing effect to generate second harmonic of the difference frequency.

In this paper, acoustic streaming generated by standing waves in a cylindrical enclosure filled with water is simulated. The effects of geometry, vibrating amplitude and frequency on formation of streaming structures are numerically investigated. The vibrating source is located at the central region of the lower plate. This source generates a plane wave at the bottom of the cylinder. The complete Navier-Stokes equations are considered and an explicit finite-difference method is used to track the acoustic waves. Water in this simulation is assumed to be a Newtonian rotational compressible single-phase liquid with an accurate equation of state. Equations are derived in Lagrangian cylindrical coordinates, using the condition of axial symmetry. The variation of acoustic pressure demonstrates a periodic modulation. The shape of the mean flow field in a period of the modulation does not differ significantly from the second period and there is a steady state condition for all periods. Results showed stronger acoustic streaming because of a decrease in enclosure height and decrease in frequencies.In addition, the increase in the enclosure radius or radius of the vibrating plate and the increase in the maximum displacement of the vibrating plate caused higher acoustic streaming velocities.

In recent period, researchers have focused on ultrasound waves which frequencies are higher than the upper limit of the human hearing range,usually around 16 or 20 kHz, in heat transfer applications because it has been found that ultrasonic waves improve heat transfer rate in heat transfer application such ass cooling applications, heat exchangers, temperature control, and so forth. Firstly, this paper presents some applications of ultrasound which related to enhancement of convective heat transfer. And also, this paper summarizes different factor which effect the heat transfer rate by ultrasound. From the literature review, it has been found that enhancement of convective heat transfer is proportional to the ultrasonic power.

The time-averaged acoustic forces acting on cylinders in a standing sound field are investigated in detail by finite volume method (FVM) numerical simulations. The forces on a cylinder in an inviscid and a viscous fluid are predicted, and the effects of viscosity are discussed. Furthermore, the secondary forces between two cylinders are also calculated. The numerical results are compared with the theoretical solutions, COMSOL software and the lattice Boltzmann (LB) method, and good agreement is achieved in most cases.

The time-averaged acoustic forces acting on cylinders in a standing sound field are investigated in detail by finite volume method (FVM) numerical simulations. The forces on a cylinder in an inviscid and a viscous fluid are predicted, and the effects of viscosity are discussed. Furthermore, the secondary forces between two cylinders are also calculated. The numerical results are compared with the theoretical solutions, COMSOL software and the lattice Boltzmann (LB) method, and good agreement is achieved in most cases.

A numerical model of ultrasonic cavitation field is described. It is based on a phenomenological description of a cavitating fluid as a non linear fluid whose characteristics (sound speed, density) depend upon the bubble density. To obtain the constitutive relationship between bubble density and acoustic pressure, a real-time measurement method of the bubble density, relying upon the variation of the electrical resistance of the medium, is proposed. The finite element formulation of the model is derived and implemented in the ATILA code. Computational results on the cavitation field created by a cylindrical concentrator are presented.

Acoustic streaming is a fundamental nonlinear phenomenon resulting from high frequency vibration in fluids. Known and investigated by Rayleigh and contemporary scientists, it attracts renewed interest due to the availability of powerful computational tools, advanced photography and precise laser velocimetry instrumentation, which can produce accurate experimental results.  Its physical mechanism however is still not clearly understood.  The analysis appears limited by the traditional premises of harmonic analysis, radiation force and wave propagation and reflection with the focus on nonlinear terms of the inertial frame formulations. Following our earlier analysis of nonlinear effects on rigid particles in a streaming fluid using time domain (TD) finite element (FE) analysis with a moving mesh via Comsol™, we present the modelling of ultrasonic streaming alone. We use state of the art laser velocimetry instrumentation to measure the average velocity of 0.5µm latex tracer particles in a 0.3-4 mms-1 streaming water insonified in the 1MHz frequency range. We use LabView™  virtual instrument to analyse light scattered by a swarm of particles in the moving fringes of crossed laser beams and find the ensemble particle motion from the frequency spectrum of the signal. In order to verify the FE modelling results with respect to the streaming velocity, the electric power is monitored at the transducer terminals. Our FE simulation, based on the Navier-Stokes (NS) equation for viscous incompressible fluids, does not involve wave propagation and radiation but is capable of representing the transient development of streaming, effects of boundaries and effects of the character of the ultrasonic source.  Our investigation shows that streaming is neither implied by a time-varying topology nor associated with the asymmetry or even with the movement of the source or the fluid surface. Surprisingly, the streaming velocity is increased by making the enclosure fully symmetrical or by using a ‘bodiless’ distributed pressure source. Observations reveal not only evolving vortices but a more complex character of streaming than generally shown, including reversed streaming. Animations  reveal transient development of a volume of streaming medium progressively ‘propagating’ away from the source and following a self contained volume of a pressure ‘valley’ travelling ahead of it and apparently attracting its motion.

"In this paper, acoustic streaming generated by standing waves in a cylindrical enclosure filled with water is simulated. The effects of geometry, vibrating amplitude and frequency on formation of streaming structures are numerically investigated. The vibrating source is located at the central region of the lower plate. This source generates a plane wave at the bottom of the cylinder. The complete Navier-Stokes equations are considered and an explicit finite-difference method is used to track the acoustic waves. Water in this simulation is assumed to be a Newtonian rotational compressible single-phase liquid with an accurate equation of state. Equations are derived in Lagrangian cylindrical coordinates, using the condition of axial symmetry. The variation of acoustic pressure demonstrates a periodic modulation. The shape of the mean flow field in a period of the modulation does not differ significantly from the second period and there is a steady state condition for all periods. Results showed stronger acoustic streaming because of a decrease in enclosure height and decrease in frequencies.In addition, the increase in the enclosure radius or radius of the vibrating plate and the increase in the maximum displacement of the vibrating plate caused higher acoustic streaming velocities.

Keywords: acoustic streaming, periodic modulation, lagrangian coordinates, nonlinear standing waves, numerical simulation, ultrasonic"