Harmonic Part

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Olivier Louisnard - One of the best experts on this subject based on the ideXlab platform.

  • a simple model of ultrasound propagation in a cavitating liquid Part i theory nonlinear attenuation and traveling wave generation
    Ultrasonics Sonochemistry, 2012
    Co-Authors: Olivier Louisnard
    Abstract:

    The bubbles involved in sonochemistry and other applications of cavitation oscillate inertially. A correct estimation of the wave attenuation in such bubbly media requires a realistic estimation of the power dissipated by the oscillation of each bubble, by thermal diffusion in the gas and viscous friction in the liquid. Both quantities and calculated numerically for a single inertial bubble driven at 20 kHz, and are found to be several orders of magnitude larger than the linear prediction. Viscous dissipation is found to be the predominant cause of energy loss for bubbles small enough. Then, the classical nonlinear Caflish equations describing the propagation of acoustic waves in a bubbly liquid are recast and simplified conveniently. The main Harmonic Part of the sound field is found to fulfill a nonlinear Helmholtz equation, where the imaginary Part of the squared wave number is directly correlated with the energy lost by a single bubble. For low acoustic driving, linear theory is recovered, but for larger drivings, namely above the Blake threshold, the attenuation coefficient is found to be more than 3 orders of magnitude larger then the linear prediction. A huge attenuation of the wave is thus expected in regions where inertial bubbles are present, which is confirmed by numerical simulations of the nonlinear Helmholtz equation in a 1D standing wave configuration. The expected strong attenuation is not only observed but furthermore, the examination of the phase between the pressure field and its gradient clearly demonstrates that a traveling wave appears in the medium.

  • a simple model of ultrasound propagation in a cavitating liquid Part i theory nonlinear attenuation and traveling wave generation
    Ultrasonics Sonochemistry, 2012
    Co-Authors: Olivier Louisnard
    Abstract:

    The bubbles involved in sonochemistry and other applications of cavitation oscillate inertially. A correct estimation of the wave attenuation in such bubbly media requires a realistic estimation of the power dissipated by the oscillation of each bubble, by thermal diffusion in the gas and viscous friction in the liquid. Both quantities and calculated numerically for a single inertial bubble driven at 20 kHz, and are found to be several orders of magnitude larger than the linear prediction. Viscous dissipation is found to be the predominant cause of energy loss for bubbles small enough. Then, the classical nonlinear Caflish equations describing the propagation of acoustic waves in a bubbly liquid are recast and simplified conveniently. The main Harmonic Part of the sound field is found to fulfill a nonlinear Helmholtz equation, where the imaginary Part of the squared wave number is directly correlated with the energy lost by a single bubble. For low acoustic driving, linear theory is recovered, but for larger drivings, namely above the Blake threshold, the attenuation coefficient ient is found to be more than 3 orders of magnitude larger then the linear prediction. A huge attenuation of the wave is thus expected in regions where inertial bubbles are present, which is confirmed by numerical simulations of the nonlinear Helmholtz equation in a 1D standing wave configuration. The expected strong attenuation is not only observed but furthermore, the examination of the phase between the pressure field and its gradient clearly demonstrates that a traveling wave appears in the medium.

Domínguez Fernandez Alejandro - One of the best experts on this subject based on the ideXlab platform.

  • Effect of grain size and density of abrasive on surface roughness, material removal rate and acoustic emission signal in rough honing processes
    'MDPI AG', 2019
    Co-Authors: Buj Corral Irene, Álvarez Flórez, Jesús Andrés, Domínguez Fernandez Alejandro
    Abstract:

    Honing processes provide a special cross-hatch pattern to the internal surface of cylinders that favors oil flow. However, along honing operation the abrasive grains wear out and lose their ability to cut material. The honing chips mixed with oil fill the pores of the abrasives and they start cutting in an incorrect way, leading to clogging. In the present paper, honing experiments were carried out according to a 32 factorial design, with different grain size and density of abrasive grains. Roughness, material removal rate, and tool wear were determined. Acoustic emissions were also measured and the chirplet concept was applied in order to detect differences between correct and incorrect cutting operations. As a general trend roughness and material removal rate increase with grain size and with density of abrasive. However, when clogging occurs roughness and material removal rate decrease, because the abrasive grains tend to deform the material instead of cutting it. When the honing process is working appropriately, the chirplet diagram of the Harmonic Part of the signal shows constant marks. On the contrary, when it does not work properly, marks disappear with time and their frequencies decrease. The results of the present paper will allow monitoring the honing process in order to change the abrasives when they are not working properly.Peer Reviewe

  • Effect of grain size and density of abrasive on surface roughness, material removal rate and acoustic emission signal in rough honing processes
    'MDPI AG', 2019
    Co-Authors: Buj Corral Irene, Álvarez Flórez, Jesús Andrés, Domínguez Fernandez Alejandro
    Abstract:

    Honing processes provide a special cross-hatch pattern to the internal surface of cylinders that favors oil flow. However, along honing operation the abrasive grains wear out and lose their ability to cut material. The honing chips mixed with oil fill the pores of the abrasives and they start cutting in an incorrect way, leading to clogging. In the present paper, honing experiments were carried out according to a 32 factorial design, with different grain size and density of abrasive grains. Roughness, material removal rate, and tool wear were determined. Acoustic emissions were also measured and the chirplet concept was applied in order to detect differences between correct and incorrect cutting operations. As a general trend roughness and material removal rate increase with grain size and with density of abrasive. However, when clogging occurs roughness and material removal rate decrease, because the abrasive grains tend to deform the material instead of cutting it. When the honing process is working appropriately, the chirplet diagram of the Harmonic Part of the signal shows constant marks. On the contrary, when it does not work properly, marks disappear with time and their frequencies decrease. The results of the present paper will allow monitoring the honing process in order to change the abrasives when they are not working properly.Peer ReviewedPostprint (published version

Qiu-shi Chen - One of the best experts on this subject based on the ideXlab platform.

  • a Harmonic fourier spectral limited area model with an external wind lateral boundary condition
    Monthly Weather Review, 1997
    Co-Authors: Qiu-shi Chen, Lesheng Bai, David H Bromwich
    Abstract:

    In comparison to the Tatsumi’s spectral method, the Harmonic-Fourier spectral method has two major advantages. 1) The semi-implicit scheme is quite efficient because the solutions of the Poisson and Helmholtz equations are readily derived. 2) The lateral boundary value problem of a limited-area model is easily solved. These advantages are the same as those of the spherical Harmonics used in global models if the singularity at the pole points for a globe is considered to be the counterPart of the lateral boundary condition for a limited region. If a limited-area model is nested in a global model, the prediction of the limited-area model at each time step is the sum of the inner Part and the Harmonic Part predictions. The inner Part prediction is solved by the double sine series from the inner Part equations for the limited-area model. The Harmonic Part prediction is derived from the prediction of the global model. An external wind lateral boundary method is proposed based on the basic property of the wind separation in a limited region. The boundary values of a limited-area model in this method are not given at the closed boundary line, but always given by Harmonic functions defined throughout the limited domain. The Harmonic functions added to the inner Parts at each time step represent the effects of the lateral boundary values on the prediction of the limited-area model, and they do not cause any discontinuity near the boundary. Tests show that predicted motion systems move smoothly in and out through the boundary, where the predicted variables are very smooth without any other boundary treatment. In addition, the boundary method can also be used in the most complicated mountainous region where the boundary intersects high mountains. The tests also show that the adiabatic dynamical Part of the limited-area model very accurately predicts the rapid development of a cyclone caused by dry baroclinic instability along the east coast of North America and a lee cyclogenesis case in East Asia. The predicted changes of intensity and location of both cyclones are close to those given by the observations.

  • A Harmonic-Sine Series Expansion and its Application to Partitioning and Reconstruction Problems in a Limited Area
    Monthly Weather Review, 1992
    Co-Authors: Qiu-shi Chen, Ying-hwa Kuo
    Abstract:

    Abstract A Harmonic-sine series expansion for a function in two-dimensional space is proposed to be a sum of two Parts. The Harmonic Part is the solution of the Laplace equation with prescribed boundary values of this function. The inner Part is the function from which the Harmonic Part has been subtracted; thus, it has zero boundary value and can be expanded by the double Fourier sine series. By using the Harmonic-sine series expansion, it is shown that only simple operations are needed to solve the Laplace, Poisson, and Helmholtz equations with a given boundary condition. The Harmonic-sine series expansion is used to solve the wind Partitioning and reconstruction problems in a limited area. The internal wind is computed from the inner Parts of the streamfunction and the velocity potential. The Harmonic wind is the difference between the observed wind and internal wind. In a limited region, the internal wind can be dealt with in the same way as the horizontal wind on the globe. The development of the vor...

Buj Corral Irene - One of the best experts on this subject based on the ideXlab platform.

  • Effect of grain size and density of abrasive on surface roughness, material removal rate and acoustic emission signal in rough honing processes
    'MDPI AG', 2019
    Co-Authors: Buj Corral Irene, Álvarez Flórez, Jesús Andrés, Domínguez Fernandez Alejandro
    Abstract:

    Honing processes provide a special cross-hatch pattern to the internal surface of cylinders that favors oil flow. However, along honing operation the abrasive grains wear out and lose their ability to cut material. The honing chips mixed with oil fill the pores of the abrasives and they start cutting in an incorrect way, leading to clogging. In the present paper, honing experiments were carried out according to a 32 factorial design, with different grain size and density of abrasive grains. Roughness, material removal rate, and tool wear were determined. Acoustic emissions were also measured and the chirplet concept was applied in order to detect differences between correct and incorrect cutting operations. As a general trend roughness and material removal rate increase with grain size and with density of abrasive. However, when clogging occurs roughness and material removal rate decrease, because the abrasive grains tend to deform the material instead of cutting it. When the honing process is working appropriately, the chirplet diagram of the Harmonic Part of the signal shows constant marks. On the contrary, when it does not work properly, marks disappear with time and their frequencies decrease. The results of the present paper will allow monitoring the honing process in order to change the abrasives when they are not working properly.Peer Reviewe

  • Effect of grain size and density of abrasive on surface roughness, material removal rate and acoustic emission signal in rough honing processes
    'MDPI AG', 2019
    Co-Authors: Buj Corral Irene, Álvarez Flórez, Jesús Andrés, Domínguez Fernandez Alejandro
    Abstract:

    Honing processes provide a special cross-hatch pattern to the internal surface of cylinders that favors oil flow. However, along honing operation the abrasive grains wear out and lose their ability to cut material. The honing chips mixed with oil fill the pores of the abrasives and they start cutting in an incorrect way, leading to clogging. In the present paper, honing experiments were carried out according to a 32 factorial design, with different grain size and density of abrasive grains. Roughness, material removal rate, and tool wear were determined. Acoustic emissions were also measured and the chirplet concept was applied in order to detect differences between correct and incorrect cutting operations. As a general trend roughness and material removal rate increase with grain size and with density of abrasive. However, when clogging occurs roughness and material removal rate decrease, because the abrasive grains tend to deform the material instead of cutting it. When the honing process is working appropriately, the chirplet diagram of the Harmonic Part of the signal shows constant marks. On the contrary, when it does not work properly, marks disappear with time and their frequencies decrease. The results of the present paper will allow monitoring the honing process in order to change the abrasives when they are not working properly.Peer ReviewedPostprint (published version

David H Bromwich - One of the best experts on this subject based on the ideXlab platform.

  • a Harmonic fourier spectral limited area model with an external wind lateral boundary condition
    Monthly Weather Review, 1997
    Co-Authors: Qiu-shi Chen, Lesheng Bai, David H Bromwich
    Abstract:

    In comparison to the Tatsumi’s spectral method, the Harmonic-Fourier spectral method has two major advantages. 1) The semi-implicit scheme is quite efficient because the solutions of the Poisson and Helmholtz equations are readily derived. 2) The lateral boundary value problem of a limited-area model is easily solved. These advantages are the same as those of the spherical Harmonics used in global models if the singularity at the pole points for a globe is considered to be the counterPart of the lateral boundary condition for a limited region. If a limited-area model is nested in a global model, the prediction of the limited-area model at each time step is the sum of the inner Part and the Harmonic Part predictions. The inner Part prediction is solved by the double sine series from the inner Part equations for the limited-area model. The Harmonic Part prediction is derived from the prediction of the global model. An external wind lateral boundary method is proposed based on the basic property of the wind separation in a limited region. The boundary values of a limited-area model in this method are not given at the closed boundary line, but always given by Harmonic functions defined throughout the limited domain. The Harmonic functions added to the inner Parts at each time step represent the effects of the lateral boundary values on the prediction of the limited-area model, and they do not cause any discontinuity near the boundary. Tests show that predicted motion systems move smoothly in and out through the boundary, where the predicted variables are very smooth without any other boundary treatment. In addition, the boundary method can also be used in the most complicated mountainous region where the boundary intersects high mountains. The tests also show that the adiabatic dynamical Part of the limited-area model very accurately predicts the rapid development of a cyclone caused by dry baroclinic instability along the east coast of North America and a lee cyclogenesis case in East Asia. The predicted changes of intensity and location of both cyclones are close to those given by the observations.