Gupta, Lodato, and Scalo (JFM, 2017) have demonstrated the existence of an equilibrium spectral energy cascade in shock waves formed as a result of continued modal thermoacoustic amplification consistent with Kolmogorov’s theory for high-Reynolds-number hydrodynamic turbulence. In this work, we develop a rigorous theory of spectral energy cascade in an ensemble of nonlinear acoustic waves, which fully develop into randomly distributed shock waves resulting in acoustic wave turbulence. In analogy to hydrodynamic turbulence, the dynamics are shown very similar to the homogeneous isotropic turbulence in a box. To elucidate the energy dynamics, we derive mathematically exact energy corollary for second order nonlinear acoustics thus identifying the second-order energy norm for acoustics. For randomly initialized nonlinear waves, the mean energy in the domain decays with a −2/3 law in time due to coalescence of shock waves. In the spectral space, the energy corollary yields analytical expressions of spectral energy, spectral energy flux, and spectral energy dissipation. We derive the spectral energy scaling laws based on the Kolmogorov length scale which corresponds to the shock thickness in acoustic wave turbulence.Gupta, Lodato, and Scalo (JFM, 2017) have demonstrated the existence of an equilibrium spectral energy cascade in shock waves formed as a result of continued modal thermoacoustic amplification consistent with Kolmogorov’s theory for high-Reynolds-number hydrodynamic turbulence. In this work, we develop a rigorous theory of spectral energy cascade in an ensemble of nonlinear acoustic waves, which fully develop into randomly distributed shock waves resulting in acoustic wave turbulence. In analogy to hydrodynamic turbulence, the dynamics are shown very similar to the homogeneous isotropic turbulence in a box. To elucidate the energy dynamics, we derive mathematically exact energy corollary for second order nonlinear acoustics thus identifying the second-order energy norm for acoustics. For randomly initialized nonlinear waves, the mean energy in the domain decays with a −2/3 law in time due to coalescence of shock waves. In the spectral space, the energy corollary yields analytical expressions of spectral e...
{"title":"Spectral energy cascade in nonlinear acoustic and thermoacoustic waves","authors":"Prateek Gupta, C. Scalo","doi":"10.1121/2.0000866","DOIUrl":"https://doi.org/10.1121/2.0000866","url":null,"abstract":"Gupta, Lodato, and Scalo (JFM, 2017) have demonstrated the existence of an equilibrium spectral energy cascade in shock waves formed as a result of continued modal thermoacoustic amplification consistent with Kolmogorov’s theory for high-Reynolds-number hydrodynamic turbulence. In this work, we develop a rigorous theory of spectral energy cascade in an ensemble of nonlinear acoustic waves, which fully develop into randomly distributed shock waves resulting in acoustic wave turbulence. In analogy to hydrodynamic turbulence, the dynamics are shown very similar to the homogeneous isotropic turbulence in a box. To elucidate the energy dynamics, we derive mathematically exact energy corollary for second order nonlinear acoustics thus identifying the second-order energy norm for acoustics. For randomly initialized nonlinear waves, the mean energy in the domain decays with a −2/3 law in time due to coalescence of shock waves. In the spectral space, the energy corollary yields analytical expressions of spectral energy, spectral energy flux, and spectral energy dissipation. We derive the spectral energy scaling laws based on the Kolmogorov length scale which corresponds to the shock thickness in acoustic wave turbulence.Gupta, Lodato, and Scalo (JFM, 2017) have demonstrated the existence of an equilibrium spectral energy cascade in shock waves formed as a result of continued modal thermoacoustic amplification consistent with Kolmogorov’s theory for high-Reynolds-number hydrodynamic turbulence. In this work, we develop a rigorous theory of spectral energy cascade in an ensemble of nonlinear acoustic waves, which fully develop into randomly distributed shock waves resulting in acoustic wave turbulence. In analogy to hydrodynamic turbulence, the dynamics are shown very similar to the homogeneous isotropic turbulence in a box. To elucidate the energy dynamics, we derive mathematically exact energy corollary for second order nonlinear acoustics thus identifying the second-order energy norm for acoustics. For randomly initialized nonlinear waves, the mean energy in the domain decays with a −2/3 law in time due to coalescence of shock waves. In the spectral space, the energy corollary yields analytical expressions of spectral e...","PeriodicalId":20469,"journal":{"name":"Proc. Meet. Acoust.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91054131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Fractures play a significant role in nonlinear wave interactions in rocks. These same fractures are fundamental to the production of geothermal energy as well as unconventional oil and gas, so understanding them has significant practical value. In this study, we examine the nonlinear interactions of P and S waves as a function of uniaxial stress. We perform a set of experiments on two sandstone samples known to have aligned fractures taken from the same quarry but cut so that the experiment is oriented differently with respect to the fractures. Complementary measurements show that the velocity decreases with stress indicating that the applied stress opens the fractures in both samples. For most of our data, we observe a significant decrease in the nonlinear response as a function of the applied stress independent of the orientation of the fractures and the experiment. An interesting exception is the coupling of two S-waves where we observe an increase in the nonlinear response at lower stresses before a decrease as the load is increased.Fractures play a significant role in nonlinear wave interactions in rocks. These same fractures are fundamental to the production of geothermal energy as well as unconventional oil and gas, so understanding them has significant practical value. In this study, we examine the nonlinear interactions of P and S waves as a function of uniaxial stress. We perform a set of experiments on two sandstone samples known to have aligned fractures taken from the same quarry but cut so that the experiment is oriented differently with respect to the fractures. Complementary measurements show that the velocity decreases with stress indicating that the applied stress opens the fractures in both samples. For most of our data, we observe a significant decrease in the nonlinear response as a function of the applied stress independent of the orientation of the fractures and the experiment. An interesting exception is the coupling of two S-waves where we observe an increase in the nonlinear response at lower stresses before a d...
{"title":"Nonlinear interactions of P and S waves under uniaxial stress","authors":"Lauren O. Hayes, A. Malcolm, K. Moravej, S. Butt","doi":"10.1121/2.0000857","DOIUrl":"https://doi.org/10.1121/2.0000857","url":null,"abstract":"Fractures play a significant role in nonlinear wave interactions in rocks. These same fractures are fundamental to the production of geothermal energy as well as unconventional oil and gas, so understanding them has significant practical value. In this study, we examine the nonlinear interactions of P and S waves as a function of uniaxial stress. We perform a set of experiments on two sandstone samples known to have aligned fractures taken from the same quarry but cut so that the experiment is oriented differently with respect to the fractures. Complementary measurements show that the velocity decreases with stress indicating that the applied stress opens the fractures in both samples. For most of our data, we observe a significant decrease in the nonlinear response as a function of the applied stress independent of the orientation of the fractures and the experiment. An interesting exception is the coupling of two S-waves where we observe an increase in the nonlinear response at lower stresses before a decrease as the load is increased.Fractures play a significant role in nonlinear wave interactions in rocks. These same fractures are fundamental to the production of geothermal energy as well as unconventional oil and gas, so understanding them has significant practical value. In this study, we examine the nonlinear interactions of P and S waves as a function of uniaxial stress. We perform a set of experiments on two sandstone samples known to have aligned fractures taken from the same quarry but cut so that the experiment is oriented differently with respect to the fractures. Complementary measurements show that the velocity decreases with stress indicating that the applied stress opens the fractures in both samples. For most of our data, we observe a significant decrease in the nonlinear response as a function of the applied stress independent of the orientation of the fractures and the experiment. An interesting exception is the coupling of two S-waves where we observe an increase in the nonlinear response at lower stresses before a d...","PeriodicalId":20469,"journal":{"name":"Proc. Meet. Acoust.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80365903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Thomas S. Jerome, Y. A. Ilinskii, E. A. Zabolotskaya, M. Hamilton
When the density and bulk modulus of a scatterer are similar to those of the surrounding liquid and the incident sound field is a standing wave, the Born approximation may be used to calculate the acoustic radiation force and torque acting on scatterers of arbitrary shape. The approximation consists of integration over the monopole and dipole contributions to the force acting on each differential volume element within the scatterer. The approach is applied to an axisymmetric scatterer, for which the force and torque may be expressed as an integral along the axis of symmetry. The integral is evaluated analytically for spherical and cylindrical scatterers. The accuracy of the Born approximation is assessed by comparison with the complete solutions for elastic spheres and prolate spheroids based on expansions of the incident and scattered fields in terms of spherical harmonics and spheroidal wave functions, respectively. Results are presented for various particle densities and bulk moduli relative to the surrounding liquid, as well as different shapes, sizes, and orientations of the particle with respect to the standing wave field.When the density and bulk modulus of a scatterer are similar to those of the surrounding liquid and the incident sound field is a standing wave, the Born approximation may be used to calculate the acoustic radiation force and torque acting on scatterers of arbitrary shape. The approximation consists of integration over the monopole and dipole contributions to the force acting on each differential volume element within the scatterer. The approach is applied to an axisymmetric scatterer, for which the force and torque may be expressed as an integral along the axis of symmetry. The integral is evaluated analytically for spherical and cylindrical scatterers. The accuracy of the Born approximation is assessed by comparison with the complete solutions for elastic spheres and prolate spheroids based on expansions of the incident and scattered fields in terms of spherical harmonics and spheroidal wave functions, re...
{"title":"Acoustic radiation force and torque on nonspherical scatterers in the Born approximation","authors":"Thomas S. Jerome, Y. A. Ilinskii, E. A. Zabolotskaya, M. Hamilton","doi":"10.1121/2.0000858","DOIUrl":"https://doi.org/10.1121/2.0000858","url":null,"abstract":"When the density and bulk modulus of a scatterer are similar to those of the surrounding liquid and the incident sound field is a standing wave, the Born approximation may be used to calculate the acoustic radiation force and torque acting on scatterers of arbitrary shape. The approximation consists of integration over the monopole and dipole contributions to the force acting on each differential volume element within the scatterer. The approach is applied to an axisymmetric scatterer, for which the force and torque may be expressed as an integral along the axis of symmetry. The integral is evaluated analytically for spherical and cylindrical scatterers. The accuracy of the Born approximation is assessed by comparison with the complete solutions for elastic spheres and prolate spheroids based on expansions of the incident and scattered fields in terms of spherical harmonics and spheroidal wave functions, respectively. Results are presented for various particle densities and bulk moduli relative to the surrounding liquid, as well as different shapes, sizes, and orientations of the particle with respect to the standing wave field.When the density and bulk modulus of a scatterer are similar to those of the surrounding liquid and the incident sound field is a standing wave, the Born approximation may be used to calculate the acoustic radiation force and torque acting on scatterers of arbitrary shape. The approximation consists of integration over the monopole and dipole contributions to the force acting on each differential volume element within the scatterer. The approach is applied to an axisymmetric scatterer, for which the force and torque may be expressed as an integral along the axis of symmetry. The integral is evaluated analytically for spherical and cylindrical scatterers. The accuracy of the Born approximation is assessed by comparison with the complete solutions for elastic spheres and prolate spheroids based on expansions of the incident and scattered fields in terms of spherical harmonics and spheroidal wave functions, re...","PeriodicalId":20469,"journal":{"name":"Proc. Meet. Acoust.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81309138","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The amplitude and loudness of conventional N-wave sonic booms vary randomly after propagating through atmospheric turbulence towards the ground. Recent studies have shown that the turbulence effect depends on the amplitude of incoming N-wave. The next generation of supersonic aircraft are designed to produce shaped booms, which are generally lower in amplitude than N-waves and contain shocks with much longer rise times. In this paper, the effect of nonlinearity on shaped sonic booms propagating through turbulence is compared with that for N-waves. Results suggest that nonlinearity may have a negligible impact on loudness variations for shaped signatures, while the impact for N-waves can be significant. Propagation is modeled by solving an augmented KZK propagation equation including the effects of diffraction, thermoviscous absorption, relaxation, nonlinearity, and wind fluctuations.The amplitude and loudness of conventional N-wave sonic booms vary randomly after propagating through atmospheric turbulence towards the ground. Recent studies have shown that the turbulence effect depends on the amplitude of incoming N-wave. The next generation of supersonic aircraft are designed to produce shaped booms, which are generally lower in amplitude than N-waves and contain shocks with much longer rise times. In this paper, the effect of nonlinearity on shaped sonic booms propagating through turbulence is compared with that for N-waves. Results suggest that nonlinearity may have a negligible impact on loudness variations for shaped signatures, while the impact for N-waves can be significant. Propagation is modeled by solving an augmented KZK propagation equation including the effects of diffraction, thermoviscous absorption, relaxation, nonlinearity, and wind fluctuations.
{"title":"Nonlinear propagation of shaped supersonic signatures through turbulence","authors":"Trevor A. Stout, V. Sparrow","doi":"10.1121/2.0000872","DOIUrl":"https://doi.org/10.1121/2.0000872","url":null,"abstract":"The amplitude and loudness of conventional N-wave sonic booms vary randomly after propagating through atmospheric turbulence towards the ground. Recent studies have shown that the turbulence effect depends on the amplitude of incoming N-wave. The next generation of supersonic aircraft are designed to produce shaped booms, which are generally lower in amplitude than N-waves and contain shocks with much longer rise times. In this paper, the effect of nonlinearity on shaped sonic booms propagating through turbulence is compared with that for N-waves. Results suggest that nonlinearity may have a negligible impact on loudness variations for shaped signatures, while the impact for N-waves can be significant. Propagation is modeled by solving an augmented KZK propagation equation including the effects of diffraction, thermoviscous absorption, relaxation, nonlinearity, and wind fluctuations.The amplitude and loudness of conventional N-wave sonic booms vary randomly after propagating through atmospheric turbulence towards the ground. Recent studies have shown that the turbulence effect depends on the amplitude of incoming N-wave. The next generation of supersonic aircraft are designed to produce shaped booms, which are generally lower in amplitude than N-waves and contain shocks with much longer rise times. In this paper, the effect of nonlinearity on shaped sonic booms propagating through turbulence is compared with that for N-waves. Results suggest that nonlinearity may have a negligible impact on loudness variations for shaped signatures, while the impact for N-waves can be significant. Propagation is modeled by solving an augmented KZK propagation equation including the effects of diffraction, thermoviscous absorption, relaxation, nonlinearity, and wind fluctuations.","PeriodicalId":20469,"journal":{"name":"Proc. Meet. Acoust.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87209544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Translational motion as well as expansion and contraction of a fluid parcel are numerically simulated using Rott equations inside a narrow tube of a stack in a thermoacoustic engine. Nonlinear effect is partially taken into account by numerically calculating the nonlinear advective derivative of particle velocity. Due to the nonlinear effect, numerical simulations result in gradual shift of mean position of a fluid parcel to higher temperature side of a stack, which is the Stokes drift. The velocity of actual acoustic streaming is the sum of the Stokes drift velocity and the mean Eulerian velocity at a fixed point estimated by experimentally or numerically. The refined numerical simulations of evaporation and condensation of water vapor in a wet stack using the model developed by the authors [J. Acoust. Soc. Am. 141, 4398-4407 (2017)] have indicated that pV work done by a fluid parcel increases by evaporation and condensation due mainly to more increase in mean volume of a fluid parcel by evaporation.
{"title":"Numerical nonlinear formulation of Rott equations for a thermoacoustic engine: Acoustic streaming and phase change","authors":"K. Yasui, N. Izu","doi":"10.1121/2.0000852","DOIUrl":"https://doi.org/10.1121/2.0000852","url":null,"abstract":"Translational motion as well as expansion and contraction of a fluid parcel are numerically simulated using Rott equations inside a narrow tube of a stack in a thermoacoustic engine. Nonlinear effect is partially taken into account by numerically calculating the nonlinear advective derivative of particle velocity. Due to the nonlinear effect, numerical simulations result in gradual shift of mean position of a fluid parcel to higher temperature side of a stack, which is the Stokes drift. The velocity of actual acoustic streaming is the sum of the Stokes drift velocity and the mean Eulerian velocity at a fixed point estimated by experimentally or numerically. The refined numerical simulations of evaporation and condensation of water vapor in a wet stack using the model developed by the authors [J. Acoust. Soc. Am. 141, 4398-4407 (2017)] have indicated that pV work done by a fluid parcel increases by evaporation and condensation due mainly to more increase in mean volume of a fluid parcel by evaporation.","PeriodicalId":20469,"journal":{"name":"Proc. Meet. Acoust.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75370933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
John P. Koulakis, Seth Pree, Alexander L. F. Thornton, Alexander S. Nguyen, S. Putterman
The interaction of high amplitude sound with density gradients in the background gas through which the sound propagates gives rise to the pycnoclinic acoustic force (PAF). This force is a generalization of acoustic radiation pressure for non-isentropic systems and is large compared to the known second-order pressure associated with sound when there is a large density change over a distance that is shorter than a wavelength. The PAF can squeeze pockets of low density gas or pull dense gas into regions of lower density. It is needed for a full understanding of Rijke and Sondhauss tubes, combustion in the presence of sound, and acoustic mixing of different density gases. A mathematical derivation is given and photographs in the literature provide evidence for its existence. The authors demonstrate an acoustic plasma trap based on these principles.The interaction of high amplitude sound with density gradients in the background gas through which the sound propagates gives rise to the pycnoclinic acoustic force (PAF). This force is a generalization of acoustic radiation pressure for non-isentropic systems and is large compared to the known second-order pressure associated with sound when there is a large density change over a distance that is shorter than a wavelength. The PAF can squeeze pockets of low density gas or pull dense gas into regions of lower density. It is needed for a full understanding of Rijke and Sondhauss tubes, combustion in the presence of sound, and acoustic mixing of different density gases. A mathematical derivation is given and photographs in the literature provide evidence for its existence. The authors demonstrate an acoustic plasma trap based on these principles.
{"title":"Pycnoclinic acoustic force","authors":"John P. Koulakis, Seth Pree, Alexander L. F. Thornton, Alexander S. Nguyen, S. Putterman","doi":"10.1121/2.0000848","DOIUrl":"https://doi.org/10.1121/2.0000848","url":null,"abstract":"The interaction of high amplitude sound with density gradients in the background gas through which the sound propagates gives rise to the pycnoclinic acoustic force (PAF). This force is a generalization of acoustic radiation pressure for non-isentropic systems and is large compared to the known second-order pressure associated with sound when there is a large density change over a distance that is shorter than a wavelength. The PAF can squeeze pockets of low density gas or pull dense gas into regions of lower density. It is needed for a full understanding of Rijke and Sondhauss tubes, combustion in the presence of sound, and acoustic mixing of different density gases. A mathematical derivation is given and photographs in the literature provide evidence for its existence. The authors demonstrate an acoustic plasma trap based on these principles.The interaction of high amplitude sound with density gradients in the background gas through which the sound propagates gives rise to the pycnoclinic acoustic force (PAF). This force is a generalization of acoustic radiation pressure for non-isentropic systems and is large compared to the known second-order pressure associated with sound when there is a large density change over a distance that is shorter than a wavelength. The PAF can squeeze pockets of low density gas or pull dense gas into regions of lower density. It is needed for a full understanding of Rijke and Sondhauss tubes, combustion in the presence of sound, and acoustic mixing of different density gases. A mathematical derivation is given and photographs in the literature provide evidence for its existence. The authors demonstrate an acoustic plasma trap based on these principles.","PeriodicalId":20469,"journal":{"name":"Proc. Meet. Acoust.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87405531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Developed as a numerical device for fast computation of shock hydrodynamics, hugonions have been successfully used for analysis of strong shock waves in non-reacting media [Lee et al., J. Acoust. Soc. Am. 140, 3435 (2016)]. Hugonions are particle-like hydrodynamic discontinuities that travel, interact with one another, and annihilate. In this paper, we demonstrate that the concept of hugonions can be extended to detonation waves in reacting media, in which the chemical reaction of positive thermicity leads to different equations of state ahead and behind the detonation shock. The Chapman-Jouguet (CJ) model of detonation is recast in such a way that the D-discussion remains the same as in the classical CJ theory while the piston problem is solved more efficiently using hugonions. Tested for both non-reacting (the Sod shock tube problem) and reacting (1-D detonation waves) media, the hugonion-based approach is shown to be superior in speed to the existing computational methods such as Godunov’s scheme.
作为一种快速计算激波流体力学的数值装置，hugonions已成功地用于分析非反应介质中的强激波[Lee et al.， J. Acoust.]。Soc。[j].农业学报，2014,34(2016)。休格子是一种类似粒子的流体力学不连续体，它们可以移动，相互作用，然后湮灭。在本文中，我们证明了hugonions的概念可以推广到反应介质中的爆震波，其中正热性的化学反应导致了爆震波前后不同的状态方程。Chapman-Jouguet (CJ)爆轰模型的重铸使得d -讨论与经典CJ理论保持一致，而活塞问题则使用hugonions更有效地解决了。对非反应(Sod激波管问题)和反应(一维爆震波)介质的测试表明，基于hugonion的方法在速度上优于现有的计算方法，如Godunov方案。
{"title":"Application of hugonions for efficient computation of shock and detonation waves","authors":"Jae-Wan Lee, W. Ohm, J. Park","doi":"10.1121/2.0000853","DOIUrl":"https://doi.org/10.1121/2.0000853","url":null,"abstract":"Developed as a numerical device for fast computation of shock hydrodynamics, hugonions have been successfully used for analysis of strong shock waves in non-reacting media [Lee et al., J. Acoust. Soc. Am. 140, 3435 (2016)]. Hugonions are particle-like hydrodynamic discontinuities that travel, interact with one another, and annihilate. In this paper, we demonstrate that the concept of hugonions can be extended to detonation waves in reacting media, in which the chemical reaction of positive thermicity leads to different equations of state ahead and behind the detonation shock. The Chapman-Jouguet (CJ) model of detonation is recast in such a way that the D-discussion remains the same as in the classical CJ theory while the piston problem is solved more efficiently using hugonions. Tested for both non-reacting (the Sod shock tube problem) and reacting (1-D detonation waves) media, the hugonion-based approach is shown to be superior in speed to the existing computational methods such as Godunov’s scheme.","PeriodicalId":20469,"journal":{"name":"Proc. Meet. Acoust.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85297471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nonlinear propagation of high intensity ultrasound beams combined with diffraction generates signal amplitude asymmetry. To try to explain this phenomenon we model the nonlinear pulse as a sum of harmonic signals. The phase of each harmonic signal differs from that of a plane wave of same frequency and same origin by a unique phase angle: the phase parameter Psi. For physical pulses, Psi varies between -pi/2 for no amplitude asymmetry and 0 for maximum asymmetry. Using numerical simulations we compute the amplitude of the harmonic components of a signal propagating nonlinearly and generated by a piston source. As the input pressure level increases, Psi gets closer to 0 at the shock distance leading to a larger peak-positive to peak-negative pressure ratio. Beyond the shock distance Psi tends faster towards -pi/2 with increasing input pressure. The variations of Psi are also linked to the 90 degree phase shift of the fundamental signal from near to far field. This phase jump contributes to the emergence of...
{"title":"On the signal amplitude asymmetry in nonlinear propagation","authors":"F. Prieur","doi":"10.1121/2.0000849","DOIUrl":"https://doi.org/10.1121/2.0000849","url":null,"abstract":"Nonlinear propagation of high intensity ultrasound beams combined with diffraction generates signal amplitude asymmetry. To try to explain this phenomenon we model the nonlinear pulse as a sum of harmonic signals. The phase of each harmonic signal differs from that of a plane wave of same frequency and same origin by a unique phase angle: the phase parameter Psi. For physical pulses, Psi varies between -pi/2 for no amplitude asymmetry and 0 for maximum asymmetry. Using numerical simulations we compute the amplitude of the harmonic components of a signal propagating nonlinearly and generated by a piston source. As the input pressure level increases, Psi gets closer to 0 at the shock distance leading to a larger peak-positive to peak-negative pressure ratio. Beyond the shock distance Psi tends faster towards -pi/2 with increasing input pressure. The variations of Psi are also linked to the 90 degree phase shift of the fundamental signal from near to far field. This phase jump contributes to the emergence of...","PeriodicalId":20469,"journal":{"name":"Proc. Meet. Acoust.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87227979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The new kind of experiments involving free vibrating crystal and space orientation of its crystallographic axes with respect to the stars are presented. The discovered “crystal-star effect” consists of changes in the vibrating crystal under the influence of cosmic radiation. It allows direct detection of the dark matter. The crystal-star nonclassical nonlinearity is demonstrated by measuring radio-frequency admittance, Y(F), from the quartz resonators near frequency F=10 MHz. The dark particles of (4+−1.5)×10E15 eV are directly detected, this energy corresponds to dark matter candidates Q-balls. The measured speed of particles in space is (249+−1.5) km/sec. One may call revealed particles “navitens” as they are energetic, invisible/unknown in experimental astronomy and high-energy physics. The changes in Y(F) are observed when specific crystallographic axis is directed toward the Sun, or Milky Way center, or star Deneb. The navitens may transfer their energy and linear momentum to a media of propagation. ...
{"title":"Direct detection of cosmic dark radiation by the crystal-star effect","authors":"I. Ostrovskii","doi":"10.1121/2.0000850","DOIUrl":"https://doi.org/10.1121/2.0000850","url":null,"abstract":"The new kind of experiments involving free vibrating crystal and space orientation of its crystallographic axes with respect to the stars are presented. The discovered “crystal-star effect” consists of changes in the vibrating crystal under the influence of cosmic radiation. It allows direct detection of the dark matter. The crystal-star nonclassical nonlinearity is demonstrated by measuring radio-frequency admittance, Y(F), from the quartz resonators near frequency F=10 MHz. The dark particles of (4+−1.5)×10E15 eV are directly detected, this energy corresponds to dark matter candidates Q-balls. The measured speed of particles in space is (249+−1.5) km/sec. One may call revealed particles “navitens” as they are energetic, invisible/unknown in experimental astronomy and high-energy physics. The changes in Y(F) are observed when specific crystallographic axis is directed toward the Sun, or Milky Way center, or star Deneb. The navitens may transfer their energy and linear momentum to a media of propagation. ...","PeriodicalId":20469,"journal":{"name":"Proc. Meet. Acoust.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81710285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
It is reasonably well accepted that cracks play a significant role in the nonlinear interactions of elastic waves, but the precise mechanism of why and how this works is less clear. Here, we simulate wave propagation to understand these mechanisms. Following existing techniques, we formulate the stress in terms of its linear and nonlinear contributions. The linear stress is the generalized Hooke’s law involving only the fourth-rank elastic stiffness tensor. The nonlinear stress comes from the product of the fourth- and sixth-rank tensors, and the spatial derivatives of the displacement vector. In a nonlinear isotropic medium, we show that the speeds of P- and S-waves generated by a time-harmonic source-function are not constant over time. In an anisotropic medium, P-wave speed is commonly estimated using effective medium theory. In the linear slip theory, we represent a crack by a displacement discontinuity embedded in an isotropic background. In a cracked medium, the estimated wave speeds show nonlinear ...
{"title":"A numerical model for the nonlinear interaction of elastic waves with cracks","authors":"H. Rusmanugroho, A. Malcolm, Meghdad Darijani","doi":"10.1121/2.0000851","DOIUrl":"https://doi.org/10.1121/2.0000851","url":null,"abstract":"It is reasonably well accepted that cracks play a significant role in the nonlinear interactions of elastic waves, but the precise mechanism of why and how this works is less clear. Here, we simulate wave propagation to understand these mechanisms. Following existing techniques, we formulate the stress in terms of its linear and nonlinear contributions. The linear stress is the generalized Hooke’s law involving only the fourth-rank elastic stiffness tensor. The nonlinear stress comes from the product of the fourth- and sixth-rank tensors, and the spatial derivatives of the displacement vector. In a nonlinear isotropic medium, we show that the speeds of P- and S-waves generated by a time-harmonic source-function are not constant over time. In an anisotropic medium, P-wave speed is commonly estimated using effective medium theory. In the linear slip theory, we represent a crack by a displacement discontinuity embedded in an isotropic background. In a cracked medium, the estimated wave speeds show nonlinear ...","PeriodicalId":20469,"journal":{"name":"Proc. Meet. Acoust.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84587484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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