Random focusing of nonlinear acoustic N-waves in fully developed turbulence: laboratory scale experiment

A laboratory experiment was conducted to study the propagation of short duration (25 μs) and high amplitude (1000 Pa) acoustic N-waves in turbulent flow. Turbulent flows with a root-mean-square value of the fluctuating velocity up to 4 m/s were generated using a bidimensional nozzle (140 × 1600 mm(2)). Energy spectra of velocity fluctuations were measured and found in good agreement with the modified von Ka?rma?n spectrum for fully developed turbulence. Spherical N-waves were generated by an electric spark source. Distorted waves were measured by four 3 mm diameter microphones placed beyond the turbulent jet. The presence of turbulence resulted in random focusing of the pulse; more than a threefold increase of peak pressures was occasionally observed. Statistics of the acoustic field parameters were evaluated as functions of the propagation distance and the level of turbulence fluctuations. It is shown that random inhomogeneities decrease the mean peak positive pressure up to 30% at 2 m from the source, double the mean rise time, and cause the arrival time about 0.3% earlier than that for corresponding conditions in still air. Probability distributions of the pressure amplitude possess autosimilarity properties with respect to the level of turbulence fluctuations.     

Modeling of an electrohydraulic lithotripter with the KZK equation.

The acoustic pressure field of an electrohydraulic extracorporeal shock wave lithotripter is modeled with a nonlinear parabolic wave equation (the KZK equation). The model accounts for diffraction, nonlinearity, and thermoviscous absorption. A numerical algorithm for solving the KZK equation in the time domain is used to model sound propagation from the mouth of the ellipsoidal reflector of the lithotripter. Propagation within the reflector is modeled with geometrical acoustics. It is shown that nonlinear distortion within the ellipsoidal reflector can play an important role for certain parameters. Calculated waveforms are compared with waveforms measured in a clinical lithotripter and good agreement is found. It is shown that the spatial location of the maximum negative pressure occurs pre-focally which suggests that the strongest cavitation activity will also be in front of the focus. Propagation of shock waves from a lithotripter with a pressure release reflector is considered and because of nonlinear propagation the focal waveform is not the inverse of the rigid reflector. Results from propagation through tissue are presented; waveforms are similar to those predicted in water except that the higher absorption in the tissue decreases the peak amplitude and lengthens the rise time of the shock.     

Turbulent jet interaction with a long rise-time pressure signature

A sonic boom signature with a long rise time has the ability to reduce the sonic boom, but it does not necessarily minimize the sonic boom at the ground level because of the real atmospheric turbulence. In this study, an effect of the turbulence on a long rise-time pressure signature was experimentally investigated in a ballistic range facility. To compare the effects of the turbulence on the long and short rise-time pressure signatures, a cone-cylinder projectile that simultaneously produces these pressure signatures was designed. The pressure waves interacted with a turbulent field generated by a circular nozzle. The turbulence effects were evaluated using flow diagnostic techniques: high-speed schlieren photography, a point-diffraction interferometer, and a pressure measurement. In spite of the fact that the long and short rise-time pressure signatures simultaneously travel through the turbulent field, the turbulence effects do not give the same contribution to these overpressures. Regarding the long rise-time pressure signature, the overpressure fluctuation due to the turbulence interaction is almost uniform, and a standard deviation 1.5 times greater than that of the no-turbulence case is observed. By contrast, a short rise-time pressure signature which passed through the same turbulent field is strongly affected by the turbulence. A standard deviation increases by a factor of 14 because of the turbulence interaction. Additionally, there is a non-correlation between the overpressure fluctuations of the long and short rise-time pressure signatures. These results deduce that the length of the rise time is important to the turbulence effects such as the shock focusing/diffracting.     

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.     

Simulation of a round supersonic combustor using wall-modeled large eddy simulation and partially-stirred reactor models

Simulations are presented for a generic, round supersonic combustor. Turbulence is modeled in the combustor using a wall-modeled large eddy simulation approach. Combustion is modeled using a small quasi-global mechanism and a more detailed skeletal mechanism. Both mechanisms are used in conjunction with two variations of the partially-stirred reactor model for sub-grid turbulence chemistry interactions. Sensitivity of the solutions to grid resolution is investigated. It is found that in order to achieve reasonable grid convergence in the mean wall pressure, the model constant that appears in the partially-stirred reactor model must be a function of both the chemistry mechanism and the grid resolution. Most of the combinations of mechanism and turbulent combustion model tested can be tuned in order to predict the location of the pre-combustion shock train and the peak mean pressure in the combustor. It is found that while the different models are able to reproduce the mean wall pressure, there are significant differences in the mean temperature and heat release rate fields. The sensitivity of the different combinations of mechanisms and partially-stirred reactor formulation is quantified and some combinations are found to be more prone to blowout. Two of the tuned models were tested across several fuel equivalence ratios with a single value of the partially-stirred reactor model constant. One model produced reasonable predictions of shock location and peak mean pressure for each equivalence ratio. The second model captured the global trends in the mean wall pressure, but was unable to quantitatively predict the shock location and peak mean pressure for all equivalence ratios tested.     

Beam propagation in a randomly inhomogeneous medium

An integrodifferential equation describing the angular distribution of beams is analyzed for a medium with random inhomogeneities. Beams are trapped because inhomogeneities give rise to wave localization at random locations and random times. The expressions obtained for the mean square deviation from the initial direction of beam propagation generalize the “3/2 law.”     

Evidence of wave front folding of sonic booms by a laboratory-scale deterministic experiment of shock waves in a heterogeneous medium

The influence of the planetary boundary layer on the sonic boom received at the ground level is known since the 1960s to be of major importance. Sonic boom propagation in a turbulent medium is characterized by an increase of the mean rise time and a huge variability. An experiment is conducted at a 1:100,000 scale in water to investigate ultrasonic shock wave interaction with a single heterogeneity. The experiment shows a very good scaling with sonic boom, concerning the size of the heterogeneities, the wave amplitude, and the rise time of the incident wave. The wave front folding associated with local focusing, and its link to the increase of the rise time, are evidenced by the experiment. The observed amplification of the peak pressure (by a factor up to 2), and increase of the rise time (by up to about one magnitude order), are in qualitative agreement with sonic boom observations. A nonlinear parabolic model is compared favorably to the experiment on axis, though the paraxial approximation turns out less precise off axis. Simulations are finally used to discriminate between nonlinear and linear propagations, showing nonlinearities affect mostly the higher harmonics that are in the audible range for sonic booms.     

Distortion of waves with profile discontinuities in the medium with a periodic transverse inhomogeneity distribution

For the purpose of describing the joint influence of nonlinear effects and refractive inhomogeneities on the evolution of intense acoustic waves, a model of the medium the local velocity of sound of which is periodic in the transverse direction and decreases in the propagation direction, which generalizes the known models of the layered medium and of the infinitesimally thin phase screen, is proposed. An exact solution is found for the wave with arbitrary initial conditions: time profile and transverse profile. The spatial wave structure in the inhomogeneous medium is calculated; it is shown that narrow high-amplitude regions are formed and the rate of nonlinear effect accumulation changes. It is shown that the amplitude of the wave at long distances from the source may differ little from its initial value due to compensation for the effects of nonlinear attenuation and of focusing by inhomogeneities. Possibilities of amplification of intense waves depending on the proportion between parameters of the wave and those of the inhomogeneous medium are studied.     

Formation of a reflected wave under propagation of a pulse with high peak intensity through a Kerr medium

Propagation through a Kerr medium of short pulses depending only on the longitudinal coordinate is investigated. High values of the peak intensity are considered for which the nonlinear part of the relative permittivity is on the order of unity. When a short pulse propagates through such a medium, the leading edge of the pulse is extended, while the trailing edge runs into the slowly propagating central part of the pulse; shock waves are generated at the trailing edge, giving rise to high spatial frequencies and backward reflected radiation. The duration of the pulse increases due to the high-frequency jet that forms at the trailing edge, and the peak intensity decreases. The spectrum of the backward reflected radiation is investigated as a function of the peak intensity of the pulse and the characteristics of the time dispersion of the medium.     

A theoretical study of cavitation generated by an extracorporeal shock wave lithotripter

The intense acoustic wave generated at the focus of an extracorporeal shock wave lithotripter is modeled as the impulse response of a parallel RLC circuit. The shock wave consists of a zero rise time positive spike that falls to 0 at 1 microsecond followed by a negative pressure component 6 microseconds long with amplitudes scaled to +1000 and -160 bars, P+ and P-, respectively. This pressure wave drives the Gilmore-Akulichev formulation for bubble dynamics; the zero-order effect of gas diffusion on bubble response is included. The negative pressure component of a 1000-bar shock wave will cause a preexisting bubble in the 1- to 10-microns range to expand to over 100 times its initial size, R0, for 250 microseconds, with a peak radius of approximately 1400 microns, then collapse very violently, emitting far UV or soft x-ray photons (black body). Gas diffusion does not appreciably mitigate the amplitude of the pressure wave radiated at the primary collapse, but does significantly reduce the collapse temperature. Diffusion also increases the bubble radius from R0 up to 40 microns and extends the duration of ringing following the primary collapse, assuming that the bubble does not break up or shed microbubbles. Results are sensitive to P+/P- and to the duration of the negative pressure cycle but not to rise time.     

超临界CO2-丙烷混合物管内传热特性数值研究

采用SST k-w湍流模型对超临界CO₂/丙烷混合工质水平管内的传热特性进行数值模拟研究。管径d=4 mm,加热段L₂=800 mm;混合工质浓度配比为100/0、95/5、90/10、85/15、80/20、75/25;质量流速为150～250 kg·m^?2·s^?1;热流密度为30～40 kW·m^?2,入口温度293 K,入口压力7.5～30 MPa。随着丙烷浓度的增加,CO₂/丙烷二元混合工质的临界压力降低,临界温度升高,丙烷浓度从5%增加到25%,换热系数峰值降低6.19%～31.45%,但增加丙烷浓度可提高拟临界温度后的换热效果。P=7.5～8.5 MPa,换热系数有明显峰值;P=20～30 MPa,换热系数变化规律无明显峰值,并随压力的升高而减小。混合工质的换热系数随质量流速的增大而增大。同一流体温度所对应的换热系数,随着热流密度的增加而减小。     

超临界CO2-丙烷混合物管内传热特性数值研究

采用SST k-w湍流模型对超临界CO₂/丙烷混合工质水平管内的传热特性进行数值模拟研究。管径d=4 mm,加热段L₂=800 mm;混合工质浓度配比为100/0、95/5、90/10、85/15、80/20、75/25;质量流速为150～250 kg·m^?2·s^?1;热流密度为30～40 kW·m^?2,入口温度293 K,入口压力7.5～30 MPa。随着丙烷浓度的增加,CO₂/丙烷二元混合工质的临界压力降低,临界温度升高,丙烷浓度从5%增加到25%,换热系数峰值降低6.19%～31.45%,但增加丙烷浓度可提高拟临界温度后的换热效果。P=7.5～8.5 MPa,换热系数有明显峰值;P=20～30 MPa,换热系数变化规律无明显峰值,并随压力的升高而减小。混合工质的换热系数随质量流速的增大而增大。同一流体温度所对应的换热系数,随着热流密度的增加而减小。     

Evolution and scaling of the peak flame surface density in spherical turbulent premixed flames subjected to decaying isotropic turbulence

The peak flame surface density within the turbulent flame brush is central to turbulent premixed combustion models in the flamelet regime. This work investigates the evolution of the peak surface density in spherically expanding turbulent premixed flames with the help of direct numerical simulations at various values of the Reynolds and Karlovitz number. The flames propagate in decaying isotropic turbulence inside a closed vessel. The effects of turbulent transport, transport due to mean velocity gradient, and flame stretch on the peak surface density are identified and characterized with an analysis based on the transport equation for the flame surface density function. The three mechanisms are governed by distinct flow time scales; turbulent transport by the eddy turnover time, mean transport by a time scale related to the pressure rise in the closed chamber, and flame stretch by the Kolmogorov time scale. Appropriate scaling of the terms is proposed and shown to collapse the data despite variations in the dimensionless groups. Overall, the transport terms lead to a reduction in the peak value of the surface density, while flame stretch has the opposite effect. In the present configuration, a small imbalance between the two leads to an exponential decay of the peak surface density in time. The dimensionless decay rate is found to be consistent with the evolution of the wrinkling scale as defined in the Bray-Moss-Libby model.     

Parabolic equation for nonlinear acoustic wave propagation in inhomogeneous moving media

A new parabolic equation is derived to describe the propagation of nonlinear sound waves in inhomogeneous moving media. The equation accounts for diffraction, nonlinearity, absorption, scalar inhomogeneities (density and sound speed), and vectorial inhomogeneities (flow). A numerical algorithm employed earlier to solve the KZK equation is adapted to this more general case. A two-dimensional version of the algorithm is used to investigate the propagation of nonlinear periodic waves in media with random inhomogeneities. For the case of scalar inhomogeneities, including the case of a flow parallel to the wave propagation direction, a complex acoustic field structure with multiple caustics is obtained. Inclusion of the transverse component of vectorial random inhomogeneities has little effect on the acoustic field. However, when a uniform transverse flow is present, the field structure is shifted without changing its morphology. The impact of nonlinearity is twofold: it produces strong shock waves in focal regions, while, outside the caustics, it produces higher harmonics without any shocks. When the intensity is averaged across the beam propagating through a random medium, it evolves similarly to the intensity of a plane nonlinear wave, indicating that the transverse redistribution of acoustic energy gives no considerable contribution to nonlinear absorption. Published in Russian in Akusticheskiĭ Zhurnal, 2006, Vol. 52, No. 6, pp. 725–735. This article was translated by the authors.     

Wavelength dependence of focusing properties of two-dimensional photonic quasicrystal flat lens

We investigated the wavelength dependence of the focusing properties of a germanium-cylinder-based two-dimensional (2D) decagonal Penrose-type photonic quasicrystal (PQC) flat lens for the first time, to the best of our knowledge. We found that near the second bandgap and in the high-frequency side (between the bandgap boundary and the first light intensity peak) of the pass band, the flat lens can exhibit a focusing effect for a point light source and that the focusing wavelengths can directly be drawn from the photonic band structure. For all the focusing wavelengths, the summation of the object distance and the image distance is less than the thickness of the flat lens when the object distance is half the thickness of the flat lens. As the wavelength increases, the image distance, the image quality, and the effective refractive index of the flat lens increase, whereas the image power of the point light source decreases. The effective refractive index of the flat lens is less than -1.     

爆炸粉末烧结颗粒间摩擦引起的界面温升研究

 针对爆炸粉末烧结过程中颗粒间的摩擦效应提出了一种无夹角斜碰撞模型,分析了烧结过程中颗粒间摩擦力随温度的变化规律,借助于LS-DYNA有限元程序研究了冲击压力、颗粒大小、材料强度等因素对孔隙闭合时间的影响,给出了颗粒界面温升的表达式。研究结果表明,由摩擦引起的颗粒界面的温升与材料特性、颗粒度、冲击角度、冲击压力等因素有关,随材料的蓄热能力、传热能力和材料强度的增加而减小,并随着材料疏松程度、颗粒直径、冲击压力的增加而增加;在粉末颗粒直径和冲击压力不是太小的情况下,颗粒表面温度将达到材料的熔点。     

气体开关抖动对单模块快脉冲直线型变压器驱动源输出特性的影响

分析了快脉冲直线型变压器驱动源(FLTD)气体开关触发击穿延时的分布规律,利用MAT-LAB软件生成随机序列模拟开关击穿延时和抖动,在FLTD简化二阶电路的基础上,利用MATLAB分析了开关抖动对40个支路并联1 MA,100 ns FLTD模块输出电流脉冲前沿和幅值的影响。模拟计算结果表明:开关理想时,即抖动为0,输出电流峰值为996 kA,峰值时间为90 ns,10%~90%脉冲前沿为54 ns;开关自身抖动与开关之间分散性之和为10 ns时,输出电流脉冲前沿增加约14%,电流峰值下降约2%;开关自身抖动与开关之间分散性之和为20 ns时,输出电流脉冲前沿增加约38%,电流峰值下降约5%。     

方截面鼓泡床气液两相瞬态数值研究

在双流体模型中引入界面浓度输运方程,利用界面浓度和气泡平均Sauter直径模化各相间作用力。引入一附加 湍动能输运方程模化气泡诱导引起的液相湍流。利用该模型对方截面鼓泡床内气液两相流进行三维瞬态数值模拟。计算结 果表明该模型能较好得模拟方截面鼓泡床内气液两相流时均和瞬态流动特征。     

The characteristics of laser‐driven shock wave investigated by time‐resolved Raman spectroscopy

An accurate and simple method, Raman peak‐shift simulation, is proposed to determine the characteristics of a laser‐driven shock wave. Using the principle of the Raman peaks shifting at high pressure and the pressure distribution in the gauge layer, the profile of the Raman peak can be numerically simulated. Combined with time‐resolved Raman spectroscopy, some main characteristics of the shock wave were determined. In the experiment, polycrystalline anthracene was used as the pressure gauge. The pump–probe technique was used to obtain the time‐resolved Raman spectra of anthracene under shock loading. The velocity of the shock wave, the peak pressure and the rise time of the shock front were determined by simulating the experimental spectra numerically. The result shows that the method of Raman peak‐shift simulation is effective in obtaining the characteristics of a laser‐driven shock wave. Copyright © 2010 John Wiley & Sons, Ltd.     

Amplitude fluctuations in the theory of radio-wave refraction scattering

We consider some aspects of the theory of radio-wave scattering with respect to studies of radiation intensity fluctuations behind a random phase screen. The expressions for a piecewise approximation of the function of distribution of intensity fluctuations in the near zone and in the region of random focusing behind the screen are found. The expressions obtained are used to calculate the radio-wave scintillation index in these regions. The corresponding calculations are performed with allowance for the finite dimensions of external and internal scales of turbulent inhomogeneities of the phase screen. It is shown that the radio-wave refraction scattering, as a rule, is characterized by a pronounced random focusing of the radiation intensity behind the phase screen. However, under strongly developed turbulence of the radio-wave propagation medium (phase screen) the above phenomenon may be absent.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 9, pp. 1114–1124, September, 1996.This paper was supported by the Russian Foundation for Fundamental Research under project 95-02-03716.