Nonlinear and diffraction effects in propagation of N-waves in randomly inhomogeneous moving media

Finite amplitude acoustic wave propagation through atmospheric turbulence is modeled using a Khokhlov-Zabolotskaya-Kuznetsov (KZK)-type equation. The equation accounts for the combined effects of nonlinearity, diffraction, absorption, and vectorial inhomogeneities of the medium. A numerical algorithm is developed which uses a shock capturing scheme to reduce the number of temporal grid points. The inhomogeneous medium is modeled using random Fourier modes technique. Propagation of N-waves through the medium produces regions of focusing and defocusing that is consistent with geometrical ray theory. However, differences up to ten wavelengths are observed in the locations of fist foci. Nonlinear effects are shown to enhance local focusing, increase the maximum peak pressure (up to 60%), and decrease the shock rise time (about 30 times). Although the peak pressure increases and the rise time decreases in focal regions, statistical analysis across the entire wavefront at a distance 120 wavelengths from the source indicates that turbulence: decreases the mean time-of-flight by 15% of a pulse duration, decreases the mean peak pressure by 6%, and increases the mean rise time by almost 100%. The peak pressure and the arrival time are primarily governed by large scale inhomogeneities, while the rise time is also sensitive to small scales.     

Experimental investigation of the travel-time variance of an acoustic wave propagating through the grid-generated turbulence

An experimental technique for the investigation of the behaviour of acoustic wave propagation through a turbulent medium is discussed. The present study utilizes the ultrasonic travel-time technique to diagnose a grid-generated turbulence. Travel-time variance is studied versus mean flow velocity, travel distance and outer turbulence scale. The effect of thermal fluctuations, which result in fluctuations of sound speed, is studied using a heated-grid experiment. Experimental data obtained using ultrasonic technique confirm numerical and theoretical predictions of nonlinear increase of the travel-time variance with propagation distance, which could be connected to the occurrence of caustics. The effect of turbulent intensity on the travel-time variance and appearance of caustics is studied. It is demonstrated experimentally that the higher turbulence intensity leads to the shorter distance, at which the first caustic occurs. The probability density for caustics appearance is analysed against the measured wave amplitude fluctuations. The analysis reveals that the region of high-amplitude fluctuations corresponds to the region where the probability of formation of random caustics differs from zero. Experimental results are in very good agreement with theoretical and numerical predictions.     

Measurement of wind noise levels in streamlined probes

This paper investigates the wind noise pressure spectra measured by aerodynamically designed devices in turbulent flow. Such measurement probes are often used in acoustic measurements in wind tunnels to reduce the pressure fluctuations generated by the interaction of the devices with the incident flow. When placed in an outdoor turbulent environment however, their performance declines noticeably. It is hypothesized that these devices are measuring the stagnation pressures generated by the cross flow components of the turbulence. Predictions for the cross flow contribution to the stagnation pressure spectra based on measured velocity spectra are developed, and are then compared to the measured pressure spectra in four different probe type devices in windy conditions outdoors. The predictions agree well with the measurements and show that the cross flow contamination coefficient is on the order of 0.5 in outdoor turbulent flows in contrast to the published value of 0.15 for measurements in a turbulent jet indoors.     

Nonlinear propagation of spark-generated N-waves in air: modeling and measurements using acoustical and optical methods

The propagation of nonlinear spherically diverging N-waves in homogeneous air is studied experimentally and theoretically. A spark source is used to generate high amplitude (1.4 kPa) short duration (40 μs) N-waves; acoustic measurements are performed using microphones (3 mm diameter, 150 kHz bandwidth). Numerical modeling with the generalized Burgers equation is used to reveal the relative effects of acoustic nonlinearity, thermoviscous absorption, and oxygen and nitrogen relaxation on the wave propagation. The results of modeling are in a good agreement with the measurements in respect to the wave amplitude and duration. However, the measured rise time of the front shock is ten times longer than the calculated one, which is attributed to the limited bandwidth of the microphone. To better resolve the shock thickness, a focused shadowgraphy technique is used. The recorded optical shadowgrams are compared with shadow patterns predicted by geometrical optics and scalar diffraction model of light propagation. It is shown that the geometrical optics approximation results in overestimation of the shock rise time, while the diffraction model allows to correctly resolve the shock width. A combination of microphone measurements and focused optical shadowgraphy is therefore a reliable way of studying evolution of spark-generated shock waves in air.     

Setting up an experimental apparatus for the study of multimodal acoustic propagation with turbulent mean flow

An experiment has been set up to study multimodal acoustic propagation inside a cylindrical duct in presence of a turbulent mean flow. This paper describes the preliminary work which has been found necessary for assembling the experiment together with first measurement results. In order to set up this experimental facility, a high level acoustic source was developed to generate higher propagating modes in the presence of mean flow. A microphonic antenna was designed for detecting the propagating modes. LDV measurements were performed and synchronous detection was used to extract both the mean flow and the acoustic components of the particle velocity. Results of aeraulic measurements are presented. Then, results of acoustic velocity measurements are compared to results obtained from the microphonic antenna.     

The mean-field method in the problem of acoustic wave propagation in a turbulent atmosphere

We analyze the problem of acoustic-wave propagation in a turbulent atmosphere using the mean-field method. The equation for the sound pressure is written with accuracy up to terms that are linear with respect to the Mach number of the turbulent air flow. An expression for the attenuation constant of the mean field is obtained. For the turbulence model described by the von Kármán correlation function of fluctuations, the attenuation coefficient of the mean field is numerically studied in detail. It is shown that under typical conditions of the near-ground atmospheric layer, the predominant contribution to scattering of acoustic waves is given by the turbulent motion of the air masses. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 5, pp. 413–424, May 2008.     

A case study of dispersion in the lee of an obstacle

Summary The influence of hills, valleys and other obstacles on the atmospheric boundary layer is such that in their lee the mean wind velocity is reduced. Intermittent or fully separated flow conditions can arise, including regions of negligible mean wind. In these conditions dispersion is driven mainly by turbulent fluctuations, which prevail over the mean motion. In this work we review the general features of mean flow and turbulence intensity in the lee of a 2D obstacle. Using published wind tunnel data, we examine a case study of dispersion from a source placed in the lee and compare the measured concentrations with those of a random walk model simulation. Paper presented at the GNFAO/EURASAP Meeting, Turin, September 1989. To speed up publication, proofs were not sent to the authors and were supervised by the Scientific Committee.     

Interaction between parallel polymer fibers insonificated by ultrasound of low/mild intensity: an analytical theory and experiments

The purpose of this article is to develop a simple mathematical model to address some bioeffects which may be caused by a static attractive force between two long neighboring parallel thin fibers (for example, a pair of collagen bundles of connective tissue) when they are insonificated by a continuous (CW) traveling plane ultrasound (US) under the condition that the fiber length (L)?the distance between them (h) and h?the wavelength of US (λ). The theory predicts that there is an attractive force between these fibers when they are exposed to the CW US with an intensity of a magnitude of 100mW/cm(2). The relationship between the relative approaching velocity of the fibers and the acoustic pressure amplitude can be calculated using the theory. An experiment was performed to verify the theoretical predictions. A plastic test chamber (diameter × height=6mm × 3.5mm) with a cap made of a sound-absorbing material and filled full with distilled water was placed on a microscope stage. A polymer fiber pair of 100μm diameter (d) and 4mm length (L) were immersed in water and aligned parallel in a plane which is normal to the US propagation direction. They floated at the central area of the chamber and h ≤10d. A 25mm diameter, 1MHz quartz crystal was used as an ultrasound source as well as the bottom of the test chamber. The quartz crystal was gold-coated on both sides, but a 5mm diameter center was left transparent (electrode free) to enable optical observation via a microscope. The maximum acoustic intensity, I(max), of the CW wave generated by the source was set at 300mW/cm(2); the corresponding acoustic pressure amplitude was 100kPa. The magnitude of the average approaching velocity of the fiber pair due to the attractive force was found in agreement with that predicted by the theory.     

快速随机粒子网格法的气动噪声预测方法

耦合随机湍流速度生成模型与线化欧拉方程技术,形成了一套具备模拟噪声在非均匀流场中传播能力的气动噪声混合预测方法。该混合方法的随机湍流速度生成模型采用了快速随机粒子网格法,为声传播模拟提供了可靠的源项。而噪声的传播计算选用线化欧拉方程,其空间离散采用9点5阶的色散保持关系格式,时间推进选用了高精度大时间步长的6级4阶龙格库塔格式,远场边界应用了无分裂形式的理想匹配层边界条件。首先,选用高斯脉冲传播算例对线化欧拉方程的时空离散格式、远场无反射边界条件进行了验证分析。然后,计算分析各向同性湍流的空间相关性验证湍流速度生成模型的可靠性。最后,基于已搭建的气动噪声混合预测方法进行了30P30N三段翼缝翼噪声的计算分析。计算分析可知:监测点处功率谱密度曲线、噪声指向性等计算结果与参考文献结果取得了较好的一致性。数值计算结果表明所建立的气动噪声混合预测方法能有效预测二维复杂构型的气动噪声问题。      

Observation of Radial Propagation of Electrostatic Fluctuations in Edge Plasma of the Sino United Spherical Tokamak

Radial propagation of electrostatic fluctuations in the edge plasma of Sino-United Spherical Tokamak (SUNIST) has been measured using Langmuir probes. The propagation characteristics of the floating potential fluctuations are analysed by the two-point correlation technique. The results show radially outward propagation of the turbulent fluctuations at all measured radial positions. The power-average wavenumber profile is approximately constant in plasma edge region and suddenly increases to the limiter. These results are in good agreement with the model predictions proposed by Mattor which suggests that the drift wave propagation may be a source of edge turbulence.     

The response of turbulent premixed flames to normal acoustic excitation

To model the thermo-acoustic excitation of flames in practical combustion systems, it is necessary to know how a turbulent flame front responds to an incident acoustic wave. This will depend partly on the way in which the burning velocity responds to the wave. In this investigation, the response of CH₄/air and CH₄/H₂/air mixtures has been observed in a novel flame stabilisation configuration, in which the premixture of fuel and air is made to decelerate under controlled conditions in a wide-angle diffuser. Control is provided by an annular wall-jet of air and by turbulence generators at the inlet. Ignition from the outlet of the diffuser allows an approximately flat flame to propagate downwards and stabilise at a height that depends on the turbulent burning velocity. When the flow is excited acoustically, the ensemble-averaged height oscillates. The fluctuations in flow velocity and flame height are monitored by phase-locked particle image velocimetry and OH-planar laser induced fluorescence, respectively. The flame stabilised against a lower incident velocity as the acoustic amplitude increased. In addition, at the lowest frequency of 52 Hz, the fluctuations in turbulent burning velocity (as represented by the displacement speed) were out-of-phase with the acoustic velocity. Thus, the rate of displacement of the flame front relative to the flow slowed as the flow accelerated, and so the flame movement was bigger than it would have been if the burning velocity had not responded to the acoustic fluctuation. With an increase in frequency to 119 Hz, the relative flame movement became even larger, although the phase-difference was reduced, so the effect on burning velocity was less dramatic. The addition of hydrogen to the methane, so as to maintain the laminar burning velocity at a lower equivalence ratio, suppressed the response at low amplitude, but at a higher amplitude, the effect was reversed.     

Autowaves in a near-threshold medium

Approximate and numerical methods are used to study the behavior of autowaves for parameters close to the propagation threshold. Under these conditions, the variations in wave velocity and amplitude are slow. A quasi-steady-state equation is derived for the velocity. This equation describes the relaxation to a steady state (uniform motion) in the above-threshold region and the initial damping stage that determines the time scale of this process in the below-threshold region. As the threshold is approached, the time scales indefinitely increase in the above-and below-threshold regions of parameters. Small random inhomogeneities of the active medium and other “ noise” sources produce intense velocity pulsations. These pulsations are comparable in scale to the mean velocity (as in the case of strong turbulence) and resemble the critical fluctuations in order parameter near the point of a continuous phase transition in their statistical properties. The pulsation spectrum exhibits a sharp peak at zero frequency. In contrast to flicker noise, this peak disappears as one recedes from the threshold. The solutions to the quasi-steady-state equation and the results of numerical simulations agree as long as the fluctuations are small— as in the theory of continuous transitions, beyond the fluctuation region.     

Sound amplitude fluctuations due to a temperature microstructure

The experiments reported in this paper were carried out in a water tank in which a random medium was generated by convective mixing from an array of heaters. An approximate thermodynamic model of the medium was derived. Temperature measurements were made which showed that the temperature microstructure created in this way could be considered as a passive additive of turbulence. Furthermore, it was possible to characterize the random refractive index in terms of a spectral distribution by using an adapted version of a spectrum proposed by Medwin for the upper ocean. By using the adapted Medwin model and the single-scatter theoretical results of Tatarski, theoretical estimates were obtained of the fluctuations of an acoustic signal propagating in this particular medium. Experiments were carried out to measure acoustic signal amplitude fluctuations at frequencies of 9 MHz and 1 MHz. The empirical results were in agreement with the theoretical estimates. Measurements are also reported for the spatial correlation functions of the acoustic signal amplitude fluctuations. The results are discussed in the light of currently available theoretical results.     

Experimental measurement of wall shear stress in strongly disrupted flows

Mean and fluctuating wall shear stress is measured in strongly disrupted cases generated by various low-porosity wall-mounted single- and multi-scale fences. These grids generate a highly turbulent wake which interacts with the wall-bounded flow modifying the wall shear stress properties. Measurement methods are validated first against a naturally growing zero pressure gradient turbulent boundary layer showing accuracies of 1% and 4% for extrapolation and direct measurement of the mean shear stress respectively. Uncertainty associated with the root mean square level of the fluctuations is better than 2% making it possible to measure small variations originating from the different fences. Additionally, probability density functions and spectra are also measured providing further insight into the flow physics. Measurement of shear stress in the disrupted cases (grid+TBL) suggest that the flow characteristics and turbulence mechanisms remain unaltered far from the grid even in the most disrupted cases. However, a different root mean square level of the fluctuations is found for different grids. Study of the probability density functions seem to imply that there are different degrees of interaction between the inner and outer regions of the flow.     

Random particle methods applied to broadband fan interaction noise

Predicting broadband fan noise is key to reduce noise emissions from aircraft and wind turbines. Complete CFD simulations of broadband fan noise generation remain too expensive to be used routinely for engineering design. A more efficient approach consists in synthesizing a turbulent velocity field that captures the main features of the exact solution. This synthetic turbulence is then used in a noise source model. This paper concentrates on predicting broadband fan noise interaction (also called leading edge noise) and demonstrates that a random particle mesh method (RPM) is well suited for simulating this source mechanism. The linearized Euler equations are used to describe sound generation and propagation. In this work, the definition of the filter kernel is generalized to include non-Gaussian filters that can directly follow more realistic energy spectra such as the ones developed by Liepmann and von Kármán. The velocity correlation and energy spectrum of the turbulence are found to be well captured by the RPM. The acoustic predictions are successfully validated against Amiet’s analytical solution for a flat plate in a turbulent stream. A standard Langevin equation is used to model temporal decorrelation, but the presence of numerical issues leads to the introduction and validation of a second-order Langevin model.     

Spherical turbulent flame propagation of pulverized coal particle clouds in an O2/N2 atmosphere

The present study aims to clarify the effects of turbulence intensity and coal concentration on the spherical turbulent flame propagation of a pulverized coal particle cloud. A unique experimental apparatus was developed in which coal particles can be dispersed homogeneously in a turbulent flow field generated by two fans. Experiments on spherical turbulent flame propagation of pulverized coal particle clouds in a constant volume spherical chamber in various turbulence intensities and coal concentrations were conducted. A common bituminous coal was used in the present study. The flame propagation velocity was obtained from an analysis of flame propagation images taken using a high-speed camera. It was found that the flame propagation velocity increased with increasing flame radius. The flame propagation velocity increases as the turbulence intensity increases. Similar trends were observed in spherical flames using gaseous fuel. The coal concentration has a weak effect on the flame propagation velocity, which is unique to pulverized coal combustions in a turbulent field. These are the first reports of experimental results for the spherical turbulent flame propagation behavior of pulverized coal particle clouds. The results obtained in the present study are obviously different from those of previous pulverized coal combustion studies and any other results of gaseous fuel combustion research.     

Intensity fluctuations of spherical acoustic waves propagating through thermal turbulence*

The intensity fluctuations of acoustic waves that propagate through thermal turbulence are investigated under well controlled laboratory conditions. Two heated grids in air are placed horizontally in a large anechoic room and the mixing of the free convection plumes above them generates a homogeneous isotropic random thermal field. The spectrum of refractive index fluctuations is accurately described by a modified von Karman model which takes into account the entire spectrum of turbulence. Experimental data are obtained by varying both the frequency of the spherical wave and the distance of propagation. In this paper we concentrate on the variance of the normalized intensity fluctuations and on their probability distributions. These measurements cover all the regimes from weak scattering to strong scattering including the peak of the intensity variance. Experimental values of the scintillation index are compared with classical theoretical predictions and also with the results of recent numerical simulations. The classical probability density functions (log-normal, exponential, I-K) are tested against the measured probability distributions. The generalized gamma distribution, which varies smoothly from log-normal to exponential as a function of two parameters, appears m represent the experimental data for a very large range of scattering conditions.     

Spherical focusing of acoustic pulses in a liquid

Nonlinear processes accompanying the focusing of a microsecond acoustic pulse produced by an electromagnetic source shaped as a spherical segment are investigated. The processes are considered to be far from the boundaries of a liquid, in the absence of cavitation. Detailed measurements of the pressure field by a fiber-optic sensor and high-speed photography of the shock front are performed. The pressure field is found to be determined by the nonlinear effects that occur in the course of the propagation of the initial converging compression wave and an edge rarefaction wave. The peak pressure amplitudes at the focus are 75 and ?42 MPa for the compression and rarefaction waves, respectively, at the maximum voltage of the pulse generator in use. The measured length of the compression wave front is equal to the response time of the sensor (8 ns). The pressure amplitude is shown to be limited by the irregularity of the propagation of a shock wave in the form of Mach’s disk. At the focus, the pressure gradient across the radiator axis reaches 0.5 atm/μm, while the diameter of the focal spot is 2.5±0.2 mm. The focus of the edge rarefaction wave formed due to diffraction is located closer to the radiator than the focus of the compression wave, which may facilitate the study of the biological effect of cavitation independently of the shear motion of the medium.     

The Alpha Effect: The Connection between Cyclonic Events and Current Helicity

In a magnetized plasma, resistive diffusion of large-scale magnetic fields can be suppressed or even overcome by a turbulently generated electromotive force. For a plasma in which the turbulence is homogeneous and isotropic this EMF is characterized by the ensemble average = ?B0, where ?v and ?b represent the turbulent fields and B0 defines the large-scale field. Determination of the statistical properties of the turbulence that are required to generate a finite alpha effect, as it has become known, is one of the central subjects of dynamo theory. Parker has shown that helical velocity fluctuations possessing a net amount of kinetic helicity are capable of dynamo action. These "cyclonic events" produce electromagnetic fluctuations characterized by their own statistical properties. Within the context of "mean-field electrodynamics" we show that these fluctuations possess a net amount of current helicity, and find that a necessary condition for dynamo action is that the turbulent current helicity and the current helicity in the large-scale field be of opposite sign.