Numerical simulations of N-wave propagation behind a random phase screen are performed based on t... more Numerical simulations of N-wave propagation behind a random phase screen are performed based on the KZK parabolic equation. One-dimensional random phase screens with fluctuations derived from Gaussian power spectrum density are considered. Numerical solutions for acoustic pressure field are obtained at various distances from the screen, before and after formation of the first focusing zones. The effects of nonlinear propagation, random focusing, and diffraction on waveform characteristics, spatial patterns, and statistical distributions of acoustic field behind the screen are investigated. Probability distribution functions for the N-wave peak pressure calculated from the numerical solutions are compared with those obtained using nonlinear geometrical acoustics (NGA) approach. It is shown that diffraction effects result in significantly different distortion of N-wave statistical distributions, as compared with the results of NGA, even at distances close to the screen.
Over the past decade, plans to develop a new generation of supersonic passenger aircrafts have sp... more Over the past decade, plans to develop a new generation of supersonic passenger aircrafts have spurred interest in sonic boom propagation in the atmosphere. New designs are focused on reducing its loudness on the ground. Sonic boom waves are affected by propagation in turbulence of the planetary boundary layer occurring in few kilometers above the ground. Therefore, sonic boom wave parameters such as peak pressure and rise time, as well as corresponding noise levels, become random, which requires statistical characterization. Theoretical analysis of the effects of the presence of turbulent layer is frequently based on one-way model equations of different complexity, of which the basic equation is the nonlinear parabolic Khokhlov-Zabolotskaya-Kuznetsov-type (KZK) equation. Here, sonic boom propagation through homogeneous isotropic turbulence is simulated using the KZK equation. Classical N-waves with different amplitudes and several examples of low-boom waveforms are considered as input waveforms at the entrance to turbulent layer. Statistical data of the peak pressure, shock front steepness, and perceived loudness metric are analyzed. It is shown than unless sonic boom amplitude exceeds a certain threshold, perceived loudness variability is mainly determined by waveform spectral components at mid-range frequencies around 100 Hz. [Work supported by RSF-18-72-00196 and ANR-10-LABX-0060/ANR-16-IDEX-0005.]
The paper presents an analytical method for calculating and analyzing the quality of 3 D acoustic... more The paper presents an analytical method for calculating and analyzing the quality of 3 D acoustic fields of multielement phased arrays used in noninvasive ultrasound surgical devices. An analytical solution for the far field of each of its elements is used when calculating the array field. This method significantly accel erates calculations while preserving the high accuracy of results as compared to conventional direct numerical integration. Radiation from typical phased arrays is calculated using this approach, and the quality of their dynamic focusing is analyzed. Undesired diffraction effects caused by electronic focus steering are consid ered: an amplitude decrease in the main maximum and the appearance of grating lobes. The quality of dynamic focusing of the acoustic fields of two practically interesting arrays with a quasi random element dis tribution (256 and 1024 elements, respectively), as well as of the regular array consisting of 256 elements is compared. In addition as well, a study is made of how the dimensions of the array elements and their spatial distributions affect the dimensions of the areas in which dynamic focusing is possible without occurrence of strong grating lobes and significant decrease in pressure amplitude at the main focus.
Propagation of nonlinear acoustic waves in inhomogeneous media is an important problem inmany res... more Propagation of nonlinear acoustic waves in inhomogeneous media is an important problem inmany research domains of modern theoretical and applied acoustics. For example, studies onpropagation of high amplitude N-waves in turbulent atmosphere are relevant to the sonic boomproblem which involves high interest due to development of new civil supersonic aircrafts. Inrelation to sonic boom problem, many studies on spark-generated N-wave propagation through aturbulent layer were carried out in model laboratory-scale experiments which are more controlledand reproducible than field measurements. Propagation of high intensity focused ultrasound intissue (HIFU) is intensively studied for medical applications. HIFU is a basis of new surgicaldevices for noninvasive thermal and mechanical ablation of tumors.In this thesis, the problem of characterization of high amplitude N-waves generated in air byan electric spark was studied using combined acoustical and optical methods. The fine structureof shocks was deduced from the shadowgraphy images with a resolution that cannot be obtainedusing condenser microphones. It was shown that the combination of optical and acoustical methodsallows complete characterization of the N-waves.N-wave propagation through a layer of thermal turbulence was further studied in a laboratoryexperiment. The evolution of statistical distributions and average values of the most importantN-wave parameters was investigated at different propagation distances. Experimental results werecompared to data obtained in another experiment known in literature, where N-wave was propagatedthrough kinematic turbulence. It was shown that in the case of almost the same widths ofthe turbulent layers, values of the characteristic scales and rms of refractive index fluctuations, thekinematic turbulence leads to stronger distortions of the peak pressure and the shock rise time ofthe N-wave and to 2-3 greater probabilities to observe intense focusing in caustics.Effects of nonlinear propagation and random focusing on the statistics of N-wave amplitudewere studied theoretically using the KZK equation and the phase screen model. The phase screenwas characterized by the correlation length and the refraction length – the distance where firstcaustics occur. Probability distributions, mean values and standard deviations of the N-wave peakpressure were obtained from the numerical solutions and were presented as functions of the propagationdistance and the nonlinear length. Statistical results from the KZK model were comparedwith analytical predictions of the nonlinear geometrical acoustics approach (NGA). It was shown,that NGA approach is valid only up to the distance of one third of refraction length of the screen.Strong nonlinear effects were shown to suppress amplitude fluctuations. The effect of the scale ofinhomogeneities on amplitude statistics was also investigated.The problem of focusing of ultrasound beam through inhomogeneous medium is importantfor medical diagnostics and nondestructive testing problems. The inhomogeneities of biologicaltissue or of industrial materials can destroy beam focusing. In the thesis, distortions of a weaklynonlinear diagnostic beam focused through a phase layer of special configuration were consideredexperimentally and theoretically. Feasibility of selective destruction of focusing of differentharmonics in the beam was predicted in the modeling and confirmed in experiment.The most modern HIFU devices rely on using two-dimensional multi-element phased arrayswith elements randomly distributed over a segment of a spherical surface. Numerical experimentis an important tool to characterize pressure fields created by HIFU radiators. Intensity levels atthe focus of HIFU radiators can reach several tens of thousands of W/cm2, causing nonlinearpropagation effects and formation of shocks [...]
The Journal of the Acoustical Society of America, 2014
ABSTRACT High intensity focused ultrasound (HIFU) is currently emerging into many clinical applic... more ABSTRACT High intensity focused ultrasound (HIFU) is currently emerging into many clinical applications. Certain HIFU modalities, histotripsy, for example, rely on the formation of high amplitude shocks in the focal waveform of the beam. These shocks develop at different focal pressure levels depending on the geometry of the HIFU transducer. The goal here was to determine optimal transducer parameters that would result in specified shock amplitudes and corresponding peak negative focal pressures. The hypothesis was that pressure level for shocks to form is mainly determined by the F-number of the transducer. As nonlinear effects accumulate almost entirely in the focal lobe of HIFU beams, shocks will form at the higher pressures for lower F-number transducers with shorter focal lobe and thus will have higher amplitudes. Simulations based on the Khokhlov-Zabolotskaya-Kuznetsov equation have shown that for typical HIFU transducers with 1-3MHz frequencies, geometries with F-number close to 1 are optimal for generating waveforms with about 70 MPa shocks and 12 MPa peak negative pressures. For lower F-number transducers, higher amplitude shocks and peak negative pressures will be formed unless cavitation occurs proximal to the focus to attenuate the focal beam. [Work supported by the grants MK-5895.2013.2, RFBR-13-02-0018, NIH-EB007643, and T32-DK007779.].
Journal of the Acoustical Society of America, 2015
The nonlinear parabolic Khokhlov-Zabolotskaya (KZ) equation is commonly used for simulation of no... more The nonlinear parabolic Khokhlov-Zabolotskaya (KZ) equation is commonly used for simulation of nonlinear focused fields generated by medical ultrasound transducers. Axially symmetric codes can be easily implemented on personal computers with simulation times on the order of tens of minutes even for the most extensive simulations of shock formation conditions. However, model accuracy can be limited for high intensity focused ultrasound sources with large convergence angles. In previous studies, it was shown that nonlinear parabolic modeling can provide good matching with measurements and full diffraction modeling in the focal region for both single element piston sources and multi-element arrays. Boundary conditions for the modeling were adjusted by varying the aperture of an equivalent planar source with a uniform pressure magnitude and a phase distribution for parabolic focusing. With this approach, there were slight discrepancies in the lateral pressure distributions in the focal plane. Here, it is prop...
The Journal of the Acoustical Society of America, 2014
The nonlinear propagation of spark-generated N-waves through thermal turbulence is experimentally... more The nonlinear propagation of spark-generated N-waves through thermal turbulence is experimentally studied at the laboratory scale under well-controlled conditions. A grid of electrical resistors was used to generate the turbulent field, well described by a modified von Kármán model. A spark source was used to generate high-amplitude (~1500 Pa) and short duration (~50 μs) N-waves. Thousands of waveforms were acquired at distances from 250 to 1750 mm from the source (~15 to 100 wavelengths). The mean values and the probability densities of the peak pressure, the deviation angle, and the rise time of the pressure wave were obtained as functions of propagation distance through turbulence. The peak pressure distributions were described using a generalized gamma distribution, whose coefficients depend on the propagation distance. A line array of microphones was used to analyze the effect of turbulence on the propagation direction. The angle of deviation induced by turbulence was found to ...
Mach stem is a well-known structure observed in the process of interaction of two strong shock wa... more Mach stem is a well-known structure observed in the process of interaction of two strong shock waves (acoustic Mach number M a > 0.1), typically in the case of reflections from a rigid boundary. However, this phenomenon has not been studied in detail for nonlinear acoustic fields that include weak shocks, i.e. for acoustic Mach number within the range from 10 -3 to 10 -2 . In acoustics, interaction of shocks can occur in case of reflections or in focusing of high power nonlinear beams. The goal of this paper was to investigate this phenomenon both numerically and experimentally for these representative cases. The KZK nonlinear evolution equation was used to demonstrate the formation of Mach stem in the focal region of periodic and pulsed beams for the Mach number of about 10 -3 . Experiments were performed in air using spark-generated N-waves reflecting from a rigid boundary. Shock fronts were visualized using Schlieren method. Regular and irregular reflections were observed and corresponding values of critical parameters for either type of reflection to occur were determined.
Numerical simulations of N-wave propagation behind a random phase screen are performed based on t... more Numerical simulations of N-wave propagation behind a random phase screen are performed based on the KZK parabolic equation. One-dimensional random phase screens with fluctuations derived from Gaussian power spectrum density are considered. Numerical solutions for acoustic pressure field are obtained at various distances from the screen, before and after formation of the first focusing zones. The effects of nonlinear propagation, random focusing, and diffraction on waveform characteristics, spatial patterns, and statistical distributions of acoustic field behind the screen are investigated. Probability distribution functions for the N-wave peak pressure calculated from the numerical solutions are compared with those obtained using nonlinear geometrical acoustics (NGA) approach. It is shown that diffraction effects result in significantly different distortion of N-wave statistical distributions, as compared with the results of NGA, even at distances close to the screen.
Over the past decade, plans to develop a new generation of supersonic passenger aircrafts have sp... more Over the past decade, plans to develop a new generation of supersonic passenger aircrafts have spurred interest in sonic boom propagation in the atmosphere. New designs are focused on reducing its loudness on the ground. Sonic boom waves are affected by propagation in turbulence of the planetary boundary layer occurring in few kilometers above the ground. Therefore, sonic boom wave parameters such as peak pressure and rise time, as well as corresponding noise levels, become random, which requires statistical characterization. Theoretical analysis of the effects of the presence of turbulent layer is frequently based on one-way model equations of different complexity, of which the basic equation is the nonlinear parabolic Khokhlov-Zabolotskaya-Kuznetsov-type (KZK) equation. Here, sonic boom propagation through homogeneous isotropic turbulence is simulated using the KZK equation. Classical N-waves with different amplitudes and several examples of low-boom waveforms are considered as input waveforms at the entrance to turbulent layer. Statistical data of the peak pressure, shock front steepness, and perceived loudness metric are analyzed. It is shown than unless sonic boom amplitude exceeds a certain threshold, perceived loudness variability is mainly determined by waveform spectral components at mid-range frequencies around 100 Hz. [Work supported by RSF-18-72-00196 and ANR-10-LABX-0060/ANR-16-IDEX-0005.]
The paper presents an analytical method for calculating and analyzing the quality of 3 D acoustic... more The paper presents an analytical method for calculating and analyzing the quality of 3 D acoustic fields of multielement phased arrays used in noninvasive ultrasound surgical devices. An analytical solution for the far field of each of its elements is used when calculating the array field. This method significantly accel erates calculations while preserving the high accuracy of results as compared to conventional direct numerical integration. Radiation from typical phased arrays is calculated using this approach, and the quality of their dynamic focusing is analyzed. Undesired diffraction effects caused by electronic focus steering are consid ered: an amplitude decrease in the main maximum and the appearance of grating lobes. The quality of dynamic focusing of the acoustic fields of two practically interesting arrays with a quasi random element dis tribution (256 and 1024 elements, respectively), as well as of the regular array consisting of 256 elements is compared. In addition as well, a study is made of how the dimensions of the array elements and their spatial distributions affect the dimensions of the areas in which dynamic focusing is possible without occurrence of strong grating lobes and significant decrease in pressure amplitude at the main focus.
Propagation of nonlinear acoustic waves in inhomogeneous media is an important problem inmany res... more Propagation of nonlinear acoustic waves in inhomogeneous media is an important problem inmany research domains of modern theoretical and applied acoustics. For example, studies onpropagation of high amplitude N-waves in turbulent atmosphere are relevant to the sonic boomproblem which involves high interest due to development of new civil supersonic aircrafts. Inrelation to sonic boom problem, many studies on spark-generated N-wave propagation through aturbulent layer were carried out in model laboratory-scale experiments which are more controlledand reproducible than field measurements. Propagation of high intensity focused ultrasound intissue (HIFU) is intensively studied for medical applications. HIFU is a basis of new surgicaldevices for noninvasive thermal and mechanical ablation of tumors.In this thesis, the problem of characterization of high amplitude N-waves generated in air byan electric spark was studied using combined acoustical and optical methods. The fine structureof shocks was deduced from the shadowgraphy images with a resolution that cannot be obtainedusing condenser microphones. It was shown that the combination of optical and acoustical methodsallows complete characterization of the N-waves.N-wave propagation through a layer of thermal turbulence was further studied in a laboratoryexperiment. The evolution of statistical distributions and average values of the most importantN-wave parameters was investigated at different propagation distances. Experimental results werecompared to data obtained in another experiment known in literature, where N-wave was propagatedthrough kinematic turbulence. It was shown that in the case of almost the same widths ofthe turbulent layers, values of the characteristic scales and rms of refractive index fluctuations, thekinematic turbulence leads to stronger distortions of the peak pressure and the shock rise time ofthe N-wave and to 2-3 greater probabilities to observe intense focusing in caustics.Effects of nonlinear propagation and random focusing on the statistics of N-wave amplitudewere studied theoretically using the KZK equation and the phase screen model. The phase screenwas characterized by the correlation length and the refraction length – the distance where firstcaustics occur. Probability distributions, mean values and standard deviations of the N-wave peakpressure were obtained from the numerical solutions and were presented as functions of the propagationdistance and the nonlinear length. Statistical results from the KZK model were comparedwith analytical predictions of the nonlinear geometrical acoustics approach (NGA). It was shown,that NGA approach is valid only up to the distance of one third of refraction length of the screen.Strong nonlinear effects were shown to suppress amplitude fluctuations. The effect of the scale ofinhomogeneities on amplitude statistics was also investigated.The problem of focusing of ultrasound beam through inhomogeneous medium is importantfor medical diagnostics and nondestructive testing problems. The inhomogeneities of biologicaltissue or of industrial materials can destroy beam focusing. In the thesis, distortions of a weaklynonlinear diagnostic beam focused through a phase layer of special configuration were consideredexperimentally and theoretically. Feasibility of selective destruction of focusing of differentharmonics in the beam was predicted in the modeling and confirmed in experiment.The most modern HIFU devices rely on using two-dimensional multi-element phased arrayswith elements randomly distributed over a segment of a spherical surface. Numerical experimentis an important tool to characterize pressure fields created by HIFU radiators. Intensity levels atthe focus of HIFU radiators can reach several tens of thousands of W/cm2, causing nonlinearpropagation effects and formation of shocks [...]
The Journal of the Acoustical Society of America, 2014
ABSTRACT High intensity focused ultrasound (HIFU) is currently emerging into many clinical applic... more ABSTRACT High intensity focused ultrasound (HIFU) is currently emerging into many clinical applications. Certain HIFU modalities, histotripsy, for example, rely on the formation of high amplitude shocks in the focal waveform of the beam. These shocks develop at different focal pressure levels depending on the geometry of the HIFU transducer. The goal here was to determine optimal transducer parameters that would result in specified shock amplitudes and corresponding peak negative focal pressures. The hypothesis was that pressure level for shocks to form is mainly determined by the F-number of the transducer. As nonlinear effects accumulate almost entirely in the focal lobe of HIFU beams, shocks will form at the higher pressures for lower F-number transducers with shorter focal lobe and thus will have higher amplitudes. Simulations based on the Khokhlov-Zabolotskaya-Kuznetsov equation have shown that for typical HIFU transducers with 1-3MHz frequencies, geometries with F-number close to 1 are optimal for generating waveforms with about 70 MPa shocks and 12 MPa peak negative pressures. For lower F-number transducers, higher amplitude shocks and peak negative pressures will be formed unless cavitation occurs proximal to the focus to attenuate the focal beam. [Work supported by the grants MK-5895.2013.2, RFBR-13-02-0018, NIH-EB007643, and T32-DK007779.].
Journal of the Acoustical Society of America, 2015
The nonlinear parabolic Khokhlov-Zabolotskaya (KZ) equation is commonly used for simulation of no... more The nonlinear parabolic Khokhlov-Zabolotskaya (KZ) equation is commonly used for simulation of nonlinear focused fields generated by medical ultrasound transducers. Axially symmetric codes can be easily implemented on personal computers with simulation times on the order of tens of minutes even for the most extensive simulations of shock formation conditions. However, model accuracy can be limited for high intensity focused ultrasound sources with large convergence angles. In previous studies, it was shown that nonlinear parabolic modeling can provide good matching with measurements and full diffraction modeling in the focal region for both single element piston sources and multi-element arrays. Boundary conditions for the modeling were adjusted by varying the aperture of an equivalent planar source with a uniform pressure magnitude and a phase distribution for parabolic focusing. With this approach, there were slight discrepancies in the lateral pressure distributions in the focal plane. Here, it is prop...
The Journal of the Acoustical Society of America, 2014
The nonlinear propagation of spark-generated N-waves through thermal turbulence is experimentally... more The nonlinear propagation of spark-generated N-waves through thermal turbulence is experimentally studied at the laboratory scale under well-controlled conditions. A grid of electrical resistors was used to generate the turbulent field, well described by a modified von Kármán model. A spark source was used to generate high-amplitude (~1500 Pa) and short duration (~50 μs) N-waves. Thousands of waveforms were acquired at distances from 250 to 1750 mm from the source (~15 to 100 wavelengths). The mean values and the probability densities of the peak pressure, the deviation angle, and the rise time of the pressure wave were obtained as functions of propagation distance through turbulence. The peak pressure distributions were described using a generalized gamma distribution, whose coefficients depend on the propagation distance. A line array of microphones was used to analyze the effect of turbulence on the propagation direction. The angle of deviation induced by turbulence was found to ...
Mach stem is a well-known structure observed in the process of interaction of two strong shock wa... more Mach stem is a well-known structure observed in the process of interaction of two strong shock waves (acoustic Mach number M a > 0.1), typically in the case of reflections from a rigid boundary. However, this phenomenon has not been studied in detail for nonlinear acoustic fields that include weak shocks, i.e. for acoustic Mach number within the range from 10 -3 to 10 -2 . In acoustics, interaction of shocks can occur in case of reflections or in focusing of high power nonlinear beams. The goal of this paper was to investigate this phenomenon both numerically and experimentally for these representative cases. The KZK nonlinear evolution equation was used to demonstrate the formation of Mach stem in the focal region of periodic and pulsed beams for the Mach number of about 10 -3 . Experiments were performed in air using spark-generated N-waves reflecting from a rigid boundary. Shock fronts were visualized using Schlieren method. Regular and irregular reflections were observed and corresponding values of critical parameters for either type of reflection to occur were determined.
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Papers by Petr Yuldashev