Single crystals subjected to shock compression exhibit responses with distinct two-wave structures for certain crystal orientations.However,little is known to date regarding how the shock response depends on crystal o...Single crystals subjected to shock compression exhibit responses with distinct two-wave structures for certain crystal orientations.However,little is known to date regarding how the shock response depends on crystal orientation,and especially why the two-wave structure depends on the crystal orientation.In this work,molecular dynamics simulations of shock compressions in copper single crystals are performed to investigate the orientation dependence of shock responses and the corresponding deformation mechanisms.Four copper single crystals with[001],[011],[012],and[123]crystal orientations along the depth direction are investigated.The[011],[012],and[123]crystal orientations of copper single crystals show distinct two-wave structures in their shock responses,while such a two-wave structure in the shock response is not seen for those orientations having a[001]crystal orientation.The potential causes are analyzed by considering the propagation velocities of both elastic and plastic waves.We develop a technique for identifying twin structures in face-centered cubic crystals and this technique can effectively identify the twin structure.The morphology of shock-induced defects(e.g.,dislocations and twins)shows the significant dependence of crystal orientation and the mechanisms behind these are discussed in detail.Finally,the Johnson-Cook constitutive model describing dynamic deformations at high temperatures and high strain rates is used to analyze the relationships between the shock responses and microscopic defects.The predictions of the Johnson-Cook constitutive model are consistent with the results of the molecular dynamics simulations.展开更多
Asymmetric plate impact experiments are conducted on LY12 aluminium alloy in a pressure range of 85-131 GPa. The longitudinal sound speeds axe obtained from the time-resolved particle speed profiles of the specimen me...Asymmetric plate impact experiments are conducted on LY12 aluminium alloy in a pressure range of 85-131 GPa. The longitudinal sound speeds axe obtained from the time-resolved particle speed profiles of the specimen measured with Velocity Interferometer System for Any Reflector (VISAR) technique, and they are shown to be good agreement with our previously reported data of this alloy in a pressure range of 20-70 GPa, and also with those of 2024 aluminium reported by McQueen. Using all of the longitudinal speeds and the corresponding bulk speeds calculated from the Gruneisen equation of state (EOS), shear moduli of LY12 aluminium alloy are obtained. A comparison of the shear moduli in the solid phase region with those estimated from the Steinberg model demonstrate that the latter are systematically lower than the measurements. By re-analysing the pressure effect on the shear modulus, a modified equation is proposed, in which the pressure term of P/η^1/3 in the Steinberg model is replaced by a linear term. Good agreement between experiments and the modified equation is obtained, which implies that the shear modulus of LY12 aluminium varies linearly both with pressure and with temperature throughout the whole solid phase region. On the other hand, shear modulus of aluminium in a solid-liquid mixed phrase region decreases gradually and smoothly, a feature that is very different from the drastic dropping at the melting point under static conditions.展开更多
The dynamic response of vitreous carbon to uniaxial strain loading has been investigated by means of the plate impact experiments. The two x cut shorted quartz gauges assembled with impactor and target were used ...The dynamic response of vitreous carbon to uniaxial strain loading has been investigated by means of the plate impact experiments. The two x cut shorted quartz gauges assembled with impactor and target were used to obtain the wave speeds in material and the stress histories at the sample gauge interface. The wave speed and stress histories were analyzed to determine the peak state in the sample. For compressive stress up to 4 0 GPa, the wave profiles were observed to be simple and steady, the uniaxial strain response is essentially nonlinear elastic, and no inelastic deformation has been found. All the experiment results indicate that the Hugoniot curve of vitreous carbon is concave downward just like that of fused silicon. There is no shock wave but the compressed wave propagating in the impacted samples.展开更多
In the paper, we study a high order numerical boundary scheme for solving the complex moving boundary problem on a fixed Cartesian mesh, and numerically investigate the moving rigid body with the complex boundary unde...In the paper, we study a high order numerical boundary scheme for solving the complex moving boundary problem on a fixed Cartesian mesh, and numerically investigate the moving rigid body with the complex boundary under the impingement of an inviscid shock wave. Based on the high order inverse Lax-Wendroff(ILW) procedure developed in the previous work(TAN, S. and SHU, C. W. A high order moving boundary treatment for compressible inviscid flows. Journal of Computational Physics, 230(15),6023–6036(2011)), in which the authors only considered the translation of the rigid body,we consider both translation and rotation of the body in this paper. In particular, we reformulate the material derivative on the moving boundary with no-penetration condition, and the newly obtained formula plays a key role in the proposed algorithm. Several numerical examples, including cylinder, elliptic cylinder, and NACA0012 airfoil, are given to indicate the effectiveness and robustness of the present method.展开更多
In this study,the dynamic compressive response behavior of a body-centered cubic(BCC)single-phase TiZrNbV refractory high-entropy alloy(RHEA)was investigated under impact at speeds of 313-1584 m s^(-1)using two-stage,...In this study,the dynamic compressive response behavior of a body-centered cubic(BCC)single-phase TiZrNbV refractory high-entropy alloy(RHEA)was investigated under impact at speeds of 313-1584 m s^(-1)using two-stage,gas-gun-driven,high-speed plate-impact experiments;recovery sample analysis;and theoretical calculations.The strain rate and pressure were approximately 10^(7) s^(−1) and 5.07-29.37 GPa,respectively.The results showed that the TiZrNbV RHEA had a Hugoniot elastic limit of 4.12-5.86 GPa and a spall strength of 1.84-2.03 GPa.The initial yield strength of the alloy showed a strong strain-rate dependence and could be described by the modified Zerilli-Armstrong model,while the phonon-damping effect was the main reason for its high strain-rate sensitivity.Microstructural analysis showed that the dynamic deformation of the TiZrNbV RHEA was controlled by the dislocation slip,dislocation proliferation,intersection of the deformation bands,and grain refinement.The analysis also showed that the intergranular,transgranular,and mixed-type cracks dominated the spall failure of the material.The dynamic Hall-Petch effect and pinning from the lattice distortion led to high dynamic yield strength.The critical strain rate for the phonon drag effect was positively related to the relative atomic mass and local strain field of the metals.Within the experimental loading range,the RHEA showed good structural stability,and simultaneously,the theoretical calculation method for the equation of state based on a cold-energy mixture could accurately predict its shock-response behavior.The valence-electron concentration(VEC)had a direct effect on the shock-compression properties of the HEAs;higher VEC implied more difficulty in compressing the HEAs.The findings of this study provide insights into understanding the mechanical response characteristics of RHEAs under extreme conditions such as high-speed impact and ultrahigh strain-rate loading.展开更多
YAG (Y_(3)Al_(5)O_(12)) transparent ceramics have attractive application prospects for transparent armor protection modules because of their excellent light transmittance and anti-ballistic capability. Understanding t...YAG (Y_(3)Al_(5)O_(12)) transparent ceramics have attractive application prospects for transparent armor protection modules because of their excellent light transmittance and anti-ballistic capability. Understanding the fracture behavior and damage mechanism of YAG is necessary for armor design. To explore the damage characteristics of YAG under compression and tension, shock compression and shockless spalling experiments with soft recovery technique are conducted. The spall strength of YAG is obtained and the recovered samples are observed by CT and SEM. It is shown that the macroscopic damage characteristic of YAG under compression is vertical split cracks with oblique fine cracks distributed in the entire sample, while that under tension is horizontal transgranular cracks concentrated near the main spall surface. The cracks generated by macroscopic compression, tension and shear stress extend in similar tensile form at the microscale. The proportion of transgranular fractures on spall surfaces is higher than that of cracks induced by macroscopic compression. Meanwhile, higher loading rate and longer loading duration increase the transgranular fracture percentage.展开更多
Combining a low temperature liquidizing system with a transient Raman spectroscopy, a new experimental technique is established for the first time on a two-stage light-gas gun, and it is employed to study shock-compre...Combining a low temperature liquidizing system with a transient Raman spectroscopy, a new experimental technique is established for the first time on a two-stage light-gas gun, and it is employed to study shock-compressed fluid silane. With this experimental technique, we first obtain a Raman peak shift relating to the Si-H stretching vibration mode of molecular liquid silane under shock loading conditions. The Raman peak of 2184 cm^-1 at an initial state of 0 GPa and 85 K moves to 2223.4 cm^-1 at a shocked state of 10.5 GPa and 950 K, and its full width of half maximum broadens from 33 cm^-1 to 118 cm^-1. The shocked temperature, calculated by the thermodynamic equation of state, is well consistent with that estimated by the Doppler broadening function.展开更多
Shock responses of Mg-Al-Zn alloy are investigated by the molecular dynamics(MD)method.The wave propagation,plastic deformation behavior and failure mechanism along the[0001]and[1010]orientations are analyzed.For both...Shock responses of Mg-Al-Zn alloy are investigated by the molecular dynamics(MD)method.The wave propagation,plastic deformation behavior and failure mechanism along the[0001]and[1010]orientations are analyzed.For both orientations,simulation results show that the shock wave has an obvious double-wave structure(plastic-elastic)under a piston velocity of 1200 m/s.A higher Hugoniot elastic limit(HEL)is observed for[0001]-oriented shock.When the shock pressure is along the[1010]direction,the distance between plastic and elastic waves is closer,and higher dislocation density and more twins are observed.Moreover,the spall strength for[1010]-oriented shock is predicted to be higher.In addition,the wave interactions,HEL and spall strength predicted for Mg-Al-Zn alloy are compared with the experimental results and MD simulation results of Mg single crystal in the literature.It is concluded that the shock performance of Mg-Al-Zn is better than that of Mg single crystal.展开更多
Tungsten has promising applications in high-radiation,high-erosion and high-impact environments.Laser peening is an effective method to enhance the surface mechanical properties of tungsten materials.However,the ultra...Tungsten has promising applications in high-radiation,high-erosion and high-impact environments.Laser peening is an effective method to enhance the surface mechanical properties of tungsten materials.However,the ultrafast dynamic mechanism of defect evolutions induced by laser shockwave in tungsten lattice is unclear.Here,we investigated the evolutions and interactions of various defects under ultrafast compressive process in tungsten lattice using molecular dynamic method.The results confirm the brittleness of tungsten and reveal that void can reduce the yield strain and strength of the tungsten lattice by accelerating defect mesh extension and promoting the dislocation nucleation around itself.Dislocation density is increased with compressive strain rate.Meanwhile,dislocation multiplication and motion reduce the elastic stage and play a dominant role during the plastic deformation of tungsten lattice.Additionally,void can disrupt the dislocation displacement and promote the pinning effect on dislocations by defect mesh extension.展开更多
In the present paper, the efficiency of an enhanced formulation of the stabilized corrective smoothed particle method (CSPM) for simulation of shock wave propagation and reflection from fixed and moving solid bounda...In the present paper, the efficiency of an enhanced formulation of the stabilized corrective smoothed particle method (CSPM) for simulation of shock wave propagation and reflection from fixed and moving solid boundaries in compressible fluids is investigated. The Lagrangian nature and its accuracy for imposing the boundary conditions are the two main reasons for adoption of CSPM. The governing equations are further modified for imposition of moving solid boundary conditions. In addition to the traditional artificial viscosity, which can remove numerically induced abnormal jumps in the field values, a velocity field smoothing technique is introduced as an efficient method for stabilizing the solution. The method has been implemented for one- and two-dimensional shock wave propagation and reflection from fixed and moving boundaries and the results have been compared with other available solutions. The method has also been adopted for simulation of shock wave propagation and reflection from infinite and finite solid boundaries.展开更多
This paper presents an experimental investigation and a theoretical analysis of cavitation control by aeration and its compressible characteristics at the flow velocity V=20m/s-50m/s. Pressure waveforms with and witho...This paper presents an experimental investigation and a theoretical analysis of cavitation control by aeration and its compressible characteristics at the flow velocity V=20m/s-50m/s. Pressure waveforms with and without aeration in cavitation region were measured. The variation of compression ratio with air concentration was described, and the relation between the least air concentration to prevent cavitation erosion and flow velocity proposed based on our experimental study. The experimental results show that aeration remarkably increases the pressure in cavitation region, and the corresponding pressure wave exhibits a compression wave/shock wave. The pressure increase in cavitation region of high-velocity flow with aeration is due to the fact that the compression waves/shock wave after the flow is aerated. The compression ratio increases with air concentration rising. The relation between flow velocity and least air concentration to prevent cavitation erosion follows a semi-cubical parabola. Also, the speed of sound and Mach number of high-velocity aerated flow were analyzed.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11972165,and 11502085)the Japan Society for the Promotion of Science(Grant No.P18067)the Fundamental Research Funds for the Central Universities of China(Grant No.2016YXMS097)。
文摘Single crystals subjected to shock compression exhibit responses with distinct two-wave structures for certain crystal orientations.However,little is known to date regarding how the shock response depends on crystal orientation,and especially why the two-wave structure depends on the crystal orientation.In this work,molecular dynamics simulations of shock compressions in copper single crystals are performed to investigate the orientation dependence of shock responses and the corresponding deformation mechanisms.Four copper single crystals with[001],[011],[012],and[123]crystal orientations along the depth direction are investigated.The[011],[012],and[123]crystal orientations of copper single crystals show distinct two-wave structures in their shock responses,while such a two-wave structure in the shock response is not seen for those orientations having a[001]crystal orientation.The potential causes are analyzed by considering the propagation velocities of both elastic and plastic waves.We develop a technique for identifying twin structures in face-centered cubic crystals and this technique can effectively identify the twin structure.The morphology of shock-induced defects(e.g.,dislocations and twins)shows the significant dependence of crystal orientation and the mechanisms behind these are discussed in detail.Finally,the Johnson-Cook constitutive model describing dynamic deformations at high temperatures and high strain rates is used to analyze the relationships between the shock responses and microscopic defects.The predictions of the Johnson-Cook constitutive model are consistent with the results of the molecular dynamics simulations.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10232040 and 10672149)the foundation of Laboratory for Shock Wave and Detonation Physics Research, China Academy of Engineering Physics (Grant No 9140C6702020603)
文摘Asymmetric plate impact experiments are conducted on LY12 aluminium alloy in a pressure range of 85-131 GPa. The longitudinal sound speeds axe obtained from the time-resolved particle speed profiles of the specimen measured with Velocity Interferometer System for Any Reflector (VISAR) technique, and they are shown to be good agreement with our previously reported data of this alloy in a pressure range of 20-70 GPa, and also with those of 2024 aluminium reported by McQueen. Using all of the longitudinal speeds and the corresponding bulk speeds calculated from the Gruneisen equation of state (EOS), shear moduli of LY12 aluminium alloy are obtained. A comparison of the shear moduli in the solid phase region with those estimated from the Steinberg model demonstrate that the latter are systematically lower than the measurements. By re-analysing the pressure effect on the shear modulus, a modified equation is proposed, in which the pressure term of P/η^1/3 in the Steinberg model is replaced by a linear term. Good agreement between experiments and the modified equation is obtained, which implies that the shear modulus of LY12 aluminium varies linearly both with pressure and with temperature throughout the whole solid phase region. On the other hand, shear modulus of aluminium in a solid-liquid mixed phrase region decreases gradually and smoothly, a feature that is very different from the drastic dropping at the melting point under static conditions.
文摘The dynamic response of vitreous carbon to uniaxial strain loading has been investigated by means of the plate impact experiments. The two x cut shorted quartz gauges assembled with impactor and target were used to obtain the wave speeds in material and the stress histories at the sample gauge interface. The wave speed and stress histories were analyzed to determine the peak state in the sample. For compressive stress up to 4 0 GPa, the wave profiles were observed to be simple and steady, the uniaxial strain response is essentially nonlinear elastic, and no inelastic deformation has been found. All the experiment results indicate that the Hugoniot curve of vitreous carbon is concave downward just like that of fused silicon. There is no shock wave but the compressed wave propagating in the impacted samples.
基金Project supported by the National Natural Science Foundation of China (Nos. 11901555, 11901213,11871448, and 11732016)the National Numerical Windtunnel Project (No. NNW2019ZT4-B10)。
文摘In the paper, we study a high order numerical boundary scheme for solving the complex moving boundary problem on a fixed Cartesian mesh, and numerically investigate the moving rigid body with the complex boundary under the impingement of an inviscid shock wave. Based on the high order inverse Lax-Wendroff(ILW) procedure developed in the previous work(TAN, S. and SHU, C. W. A high order moving boundary treatment for compressible inviscid flows. Journal of Computational Physics, 230(15),6023–6036(2011)), in which the authors only considered the translation of the rigid body,we consider both translation and rotation of the body in this paper. In particular, we reformulate the material derivative on the moving boundary with no-penetration condition, and the newly obtained formula plays a key role in the proposed algorithm. Several numerical examples, including cylinder, elliptic cylinder, and NACA0012 airfoil, are given to indicate the effectiveness and robustness of the present method.
基金This study was financially supported by the Hunan Provin-cial Natural Science Foundation of China(Grant No.2022JJ10058)the National Natural Science Foundation of China(Grant Nos.12072369 and 52171166).The authors thank Dr.Xuehao Zheng from the ZKKF(Beijing)Science and Technology Company of China for supporting the SEM and TEM analyses.The authors would like to acknowledge Dr.Xiang Wu from KAIPLE Centre for Microscopy,Characterisation&Analysis(CMCA)of China for supporting the EBSD analyzes.
文摘In this study,the dynamic compressive response behavior of a body-centered cubic(BCC)single-phase TiZrNbV refractory high-entropy alloy(RHEA)was investigated under impact at speeds of 313-1584 m s^(-1)using two-stage,gas-gun-driven,high-speed plate-impact experiments;recovery sample analysis;and theoretical calculations.The strain rate and pressure were approximately 10^(7) s^(−1) and 5.07-29.37 GPa,respectively.The results showed that the TiZrNbV RHEA had a Hugoniot elastic limit of 4.12-5.86 GPa and a spall strength of 1.84-2.03 GPa.The initial yield strength of the alloy showed a strong strain-rate dependence and could be described by the modified Zerilli-Armstrong model,while the phonon-damping effect was the main reason for its high strain-rate sensitivity.Microstructural analysis showed that the dynamic deformation of the TiZrNbV RHEA was controlled by the dislocation slip,dislocation proliferation,intersection of the deformation bands,and grain refinement.The analysis also showed that the intergranular,transgranular,and mixed-type cracks dominated the spall failure of the material.The dynamic Hall-Petch effect and pinning from the lattice distortion led to high dynamic yield strength.The critical strain rate for the phonon drag effect was positively related to the relative atomic mass and local strain field of the metals.Within the experimental loading range,the RHEA showed good structural stability,and simultaneously,the theoretical calculation method for the equation of state based on a cold-energy mixture could accurately predict its shock-response behavior.The valence-electron concentration(VEC)had a direct effect on the shock-compression properties of the HEAs;higher VEC implied more difficulty in compressing the HEAs.The findings of this study provide insights into understanding the mechanical response characteristics of RHEAs under extreme conditions such as high-speed impact and ultrahigh strain-rate loading.
基金This work is funded by the National Natural Science Foundation of China(No.11772159)the NSAF Joint Fund(No.U1730101)the Fundamental Research Funds for the Central Universities(No.30917011104).
文摘YAG (Y_(3)Al_(5)O_(12)) transparent ceramics have attractive application prospects for transparent armor protection modules because of their excellent light transmittance and anti-ballistic capability. Understanding the fracture behavior and damage mechanism of YAG is necessary for armor design. To explore the damage characteristics of YAG under compression and tension, shock compression and shockless spalling experiments with soft recovery technique are conducted. The spall strength of YAG is obtained and the recovered samples are observed by CT and SEM. It is shown that the macroscopic damage characteristic of YAG under compression is vertical split cracks with oblique fine cracks distributed in the entire sample, while that under tension is horizontal transgranular cracks concentrated near the main spall surface. The cracks generated by macroscopic compression, tension and shear stress extend in similar tensile form at the microscale. The proportion of transgranular fractures on spall surfaces is higher than that of cracks induced by macroscopic compression. Meanwhile, higher loading rate and longer loading duration increase the transgranular fracture percentage.
基金supported by the National Natural Science Foundation of China(Grant Nos.11574254 and 11272296)the National Basic Research Program of China(Grant No.2011CB808201)+2 种基金the Fundamental Research Fund for the Central Universities,China(Grant No.2682014ZT31)the Scientific Research Plan Projects of Shannxi Provincial Education Department,China(Grant No.16JK1361)the Scientific and Technological Research Program of Chongqing Municipal Education Commission,China(Grant No.KJ1600520)
文摘Combining a low temperature liquidizing system with a transient Raman spectroscopy, a new experimental technique is established for the first time on a two-stage light-gas gun, and it is employed to study shock-compressed fluid silane. With this experimental technique, we first obtain a Raman peak shift relating to the Si-H stretching vibration mode of molecular liquid silane under shock loading conditions. The Raman peak of 2184 cm^-1 at an initial state of 0 GPa and 85 K moves to 2223.4 cm^-1 at a shocked state of 10.5 GPa and 950 K, and its full width of half maximum broadens from 33 cm^-1 to 118 cm^-1. The shocked temperature, calculated by the thermodynamic equation of state, is well consistent with that estimated by the Doppler broadening function.
基金This research are funded by the National Natural Science Foundation of China(11402183,51604206 and 51974217)the Fundamental Research Funds for the Central Universities of China(WUT:2017IA002)National Defense Science and technology foundation strengthening program.
文摘Shock responses of Mg-Al-Zn alloy are investigated by the molecular dynamics(MD)method.The wave propagation,plastic deformation behavior and failure mechanism along the[0001]and[1010]orientations are analyzed.For both orientations,simulation results show that the shock wave has an obvious double-wave structure(plastic-elastic)under a piston velocity of 1200 m/s.A higher Hugoniot elastic limit(HEL)is observed for[0001]-oriented shock.When the shock pressure is along the[1010]direction,the distance between plastic and elastic waves is closer,and higher dislocation density and more twins are observed.Moreover,the spall strength for[1010]-oriented shock is predicted to be higher.In addition,the wave interactions,HEL and spall strength predicted for Mg-Al-Zn alloy are compared with the experimental results and MD simulation results of Mg single crystal in the literature.It is concluded that the shock performance of Mg-Al-Zn is better than that of Mg single crystal.
基金financially support from the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDA25040201)the National Natural Science Foundation of China(Grant No.51727901)support provided by the Deanship of Scientific Research(DSR)at King Fahd University of Petroleum&Minerals(KFUPM)(Grant No.DF201020)
文摘Tungsten has promising applications in high-radiation,high-erosion and high-impact environments.Laser peening is an effective method to enhance the surface mechanical properties of tungsten materials.However,the ultrafast dynamic mechanism of defect evolutions induced by laser shockwave in tungsten lattice is unclear.Here,we investigated the evolutions and interactions of various defects under ultrafast compressive process in tungsten lattice using molecular dynamic method.The results confirm the brittleness of tungsten and reveal that void can reduce the yield strain and strength of the tungsten lattice by accelerating defect mesh extension and promoting the dislocation nucleation around itself.Dislocation density is increased with compressive strain rate.Meanwhile,dislocation multiplication and motion reduce the elastic stage and play a dominant role during the plastic deformation of tungsten lattice.Additionally,void can disrupt the dislocation displacement and promote the pinning effect on dislocations by defect mesh extension.
文摘In the present paper, the efficiency of an enhanced formulation of the stabilized corrective smoothed particle method (CSPM) for simulation of shock wave propagation and reflection from fixed and moving solid boundaries in compressible fluids is investigated. The Lagrangian nature and its accuracy for imposing the boundary conditions are the two main reasons for adoption of CSPM. The governing equations are further modified for imposition of moving solid boundary conditions. In addition to the traditional artificial viscosity, which can remove numerically induced abnormal jumps in the field values, a velocity field smoothing technique is introduced as an efficient method for stabilizing the solution. The method has been implemented for one- and two-dimensional shock wave propagation and reflection from fixed and moving boundaries and the results have been compared with other available solutions. The method has also been adopted for simulation of shock wave propagation and reflection from infinite and finite solid boundaries.
基金Project supported by the National Natural Science Foundation of China (Grant No: 50279048).
文摘This paper presents an experimental investigation and a theoretical analysis of cavitation control by aeration and its compressible characteristics at the flow velocity V=20m/s-50m/s. Pressure waveforms with and without aeration in cavitation region were measured. The variation of compression ratio with air concentration was described, and the relation between the least air concentration to prevent cavitation erosion and flow velocity proposed based on our experimental study. The experimental results show that aeration remarkably increases the pressure in cavitation region, and the corresponding pressure wave exhibits a compression wave/shock wave. The pressure increase in cavitation region of high-velocity flow with aeration is due to the fact that the compression waves/shock wave after the flow is aerated. The compression ratio increases with air concentration rising. The relation between flow velocity and least air concentration to prevent cavitation erosion follows a semi-cubical parabola. Also, the speed of sound and Mach number of high-velocity aerated flow were analyzed.