A theoretical model is proposed to describe the mechanism of laser-induced plasma shock wave evolution in air. To verify the validity of the theoretical model, an optical beam deflection technique is employed to track...A theoretical model is proposed to describe the mechanism of laser-induced plasma shock wave evolution in air. To verify the validity of the theoretical model, an optical beam deflection technique is employed to track the plasma shock wave evolution process. The theoretical model and the experimental signals are found to be in good agreement with each other. It is shown that the laser-induced plasma shock wave undergoes formation, increase and decay processes; the increase and the decay processes of the laser-induced plasma shock wave result from the overlapping of the compression wave and the rarefaction wave, respectively. In addition, the laser-induced plasma shock wave speed and pressure distributions, both a function of distance, are presented.展开更多
Based on the Timoshenko beam theory, the finite-deflection and the axial inertia are taken into account, and the nonlinear partial differential equations for flexural waves in a beam are derived. Using the traveling w...Based on the Timoshenko beam theory, the finite-deflection and the axial inertia are taken into account, and the nonlinear partial differential equations for flexural waves in a beam are derived. Using the traveling wave method and integration skills, the nonlinear partial differential equations can be converted into an ordinary differential equation. The qualitative analysis indicates that the corresponding dynamic system has a heteroclinic orbit under a certain condition. An exact periodic solution of the nonlinear wave equation is obtained using the Jacobi elliptic function expansion. When the modulus of the Jacobi elliptic function tends to one in the degenerate case, a shock wave solution is given. The small perturbations are further introduced, arising from the damping and the external load to an original Hamilton system, and the threshold condition of the existence of the transverse heteroclinic point is obtained using Melnikov＇s method. It is shown that the perturbed system has a chaotic property under the Smale horseshoe transform.展开更多
The shock wave angle and depth ratio of the abrupt deflected supercritical water flow due to deflector was investigated experimentally and theoretically. A correction coefficient of the hydro-dynamic pressure ξ was i...The shock wave angle and depth ratio of the abrupt deflected supercritical water flow due to deflector was investigated experimentally and theoretically. A correction coefficient of the hydro-dynamic pressure ξ was introduced to generalize the momentum equation in the perpendicular direction to the shock front. An extensive series of tests were conducted in a 1 m wide flume with the Froude number ranging from 1.70 to 8.37, the deflection angle ranging from 5° to 40° and the length of deflector ranging from 0.28 m to 1 m. A dimensionless parameter K was defined to depict the ratio of the flow height to flow thickness. Test results show that the val ue of ~, the correction coefficient of the non-hydrostatic pres- sure distribution, decreases with the increase of the value of K An empirical relationship between the value of ξ and the val ue of K was proposed. It is indicated that the relative errors of the results calculated by the revised theory is much smaller than that obtained from the Ippen theory. Finally, a simple explicit expression was suggested to calculate the shock wave height ratio in consideration of the effect of the non-hydrostatic pressure distribution.展开更多
The effect of the bottom slope on abrupt deflected supercritical water flow was experimentally and theoretically studied. Model tests were conducted in a flume of 1.2 m wide and 2.6 m long with sloped bottom at an ang...The effect of the bottom slope on abrupt deflected supercritical water flow was experimentally and theoretically studied. Model tests were conducted in a flume of 1.2 m wide and 2.6 m long with sloped bottom at an angle 35.54°, its length of deflector was 0.2 m and the deflection angles were 15° and 30°. An approximate method for calculating the shock wave angle and depth ratio of the abrupt deflected supercritical water flow was suggested, and a correction coefficient for the hydrodynamic pressure was introduced to generalize the momentum equation in the direction perpendicular to the shock front. It must be noticed that in the sloped channel the shock wave angle and the depth ratio are no longer constant as those in the horizontal channels, but slowly change along the shock front. The calculated results are in good agreement with measured data.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos 60578015,60778007 and 60878037)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(Grant No 05KTB510028)the Scientific Research Starting Foundation for Returned Scholars,Nanjing University of Posts & Telecommunications,China(Grant Nos NY207030 and NY206076)
文摘A theoretical model is proposed to describe the mechanism of laser-induced plasma shock wave evolution in air. To verify the validity of the theoretical model, an optical beam deflection technique is employed to track the plasma shock wave evolution process. The theoretical model and the experimental signals are found to be in good agreement with each other. It is shown that the laser-induced plasma shock wave undergoes formation, increase and decay processes; the increase and the decay processes of the laser-induced plasma shock wave result from the overlapping of the compression wave and the rarefaction wave, respectively. In addition, the laser-induced plasma shock wave speed and pressure distributions, both a function of distance, are presented.
基金Project supported by the National Natural Science Foundation of China (No. 10772129)
文摘Based on the Timoshenko beam theory, the finite-deflection and the axial inertia are taken into account, and the nonlinear partial differential equations for flexural waves in a beam are derived. Using the traveling wave method and integration skills, the nonlinear partial differential equations can be converted into an ordinary differential equation. The qualitative analysis indicates that the corresponding dynamic system has a heteroclinic orbit under a certain condition. An exact periodic solution of the nonlinear wave equation is obtained using the Jacobi elliptic function expansion. When the modulus of the Jacobi elliptic function tends to one in the degenerate case, a shock wave solution is given. The small perturbations are further introduced, arising from the damping and the external load to an original Hamilton system, and the threshold condition of the existence of the transverse heteroclinic point is obtained using Melnikov＇s method. It is shown that the perturbed system has a chaotic property under the Smale horseshoe transform.
文摘The shock wave angle and depth ratio of the abrupt deflected supercritical water flow due to deflector was investigated experimentally and theoretically. A correction coefficient of the hydro-dynamic pressure ξ was introduced to generalize the momentum equation in the perpendicular direction to the shock front. An extensive series of tests were conducted in a 1 m wide flume with the Froude number ranging from 1.70 to 8.37, the deflection angle ranging from 5° to 40° and the length of deflector ranging from 0.28 m to 1 m. A dimensionless parameter K was defined to depict the ratio of the flow height to flow thickness. Test results show that the val ue of ~, the correction coefficient of the non-hydrostatic pres- sure distribution, decreases with the increase of the value of K An empirical relationship between the value of ξ and the val ue of K was proposed. It is indicated that the relative errors of the results calculated by the revised theory is much smaller than that obtained from the Ippen theory. Finally, a simple explicit expression was suggested to calculate the shock wave height ratio in consideration of the effect of the non-hydrostatic pressure distribution.
基金the Natural Science Foundation of Liaoning Province (Grant No.20062177)
文摘The effect of the bottom slope on abrupt deflected supercritical water flow was experimentally and theoretically studied. Model tests were conducted in a flume of 1.2 m wide and 2.6 m long with sloped bottom at an angle 35.54°, its length of deflector was 0.2 m and the deflection angles were 15° and 30°. An approximate method for calculating the shock wave angle and depth ratio of the abrupt deflected supercritical water flow was suggested, and a correction coefficient for the hydrodynamic pressure was introduced to generalize the momentum equation in the direction perpendicular to the shock front. It must be noticed that in the sloped channel the shock wave angle and the depth ratio are no longer constant as those in the horizontal channels, but slowly change along the shock front. The calculated results are in good agreement with measured data.
