2007 Vol. 27, No. 6
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2007, 27(6): 481-486.
doi: 10.11883/1001-1455(2007)06-0481-06
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Abstract:
A phenomenological model, including nonlinear elasticity (equation of state), rate-dependent plasticity, and void nucleation and growth, was proposed to simulate deformations of U-6%Nb alloy under the condition of high strain rate. The diagonally implicit Runge-Kutta (DIRK) method was used to solve the constitutive rate equations, and stability and accuracy of the solution to thermoviscoplastic constitutive relations were improved. The proposed model was used to simulate the plate impact experiments on U-6%Nb alloy by Tonks D L, et al. Calculated results by the proposed model are in better agreement with the experimental data than the simulated results by Addessio F L, et al.
A phenomenological model, including nonlinear elasticity (equation of state), rate-dependent plasticity, and void nucleation and growth, was proposed to simulate deformations of U-6%Nb alloy under the condition of high strain rate. The diagonally implicit Runge-Kutta (DIRK) method was used to solve the constitutive rate equations, and stability and accuracy of the solution to thermoviscoplastic constitutive relations were improved. The proposed model was used to simulate the plate impact experiments on U-6%Nb alloy by Tonks D L, et al. Calculated results by the proposed model are in better agreement with the experimental data than the simulated results by Addessio F L, et al.
2007, 27(6): 487-482.
doi: 10.11883/1001-1455(2007)06-0487-06
Abstract:
A test tube is designed to experimentally evaluate the accidental explosion of a H2-He heat exchanger in a nuclear reactor when hydrogen leaks during work. The test tube is identical to the exchanger in size and geometry. In the experiments, H2-air mixture is filled into the tube at the different initial pressures and equivalence ratios. A spark igniter is located at the top of the designed tube. The transient pressure and data acquisition systems were used to record the pressure histories at the specified stations. Results show that deflagration can occur at the tops of the vacuum tube and the coolant box and characteristics of shock wave can be seen from pressure curves at neighboring test points. The shock waves pass through the slot between the coolant box and the tube side-wall and propagate into the divergent section to develop deflagration. The induced shock wave reflects on the end wall of the tube. The backward propagating shock interacts with the forward traveling flame following the shock wave initially, and the complex shock wave field can be generated. Compared with the stand atmospheric pressure, in the case of low initial pressure and rich fuel mixtures, combustion rather than deflagration occurs at the top of the tube, the pressure of the high-temperature gas rises lowly, and the pressure history does not appear at the shock wave character. The fuel-riched products move into the divergent section of the tube and are re-ignited to induce strong detonation.
A test tube is designed to experimentally evaluate the accidental explosion of a H2-He heat exchanger in a nuclear reactor when hydrogen leaks during work. The test tube is identical to the exchanger in size and geometry. In the experiments, H2-air mixture is filled into the tube at the different initial pressures and equivalence ratios. A spark igniter is located at the top of the designed tube. The transient pressure and data acquisition systems were used to record the pressure histories at the specified stations. Results show that deflagration can occur at the tops of the vacuum tube and the coolant box and characteristics of shock wave can be seen from pressure curves at neighboring test points. The shock waves pass through the slot between the coolant box and the tube side-wall and propagate into the divergent section to develop deflagration. The induced shock wave reflects on the end wall of the tube. The backward propagating shock interacts with the forward traveling flame following the shock wave initially, and the complex shock wave field can be generated. Compared with the stand atmospheric pressure, in the case of low initial pressure and rich fuel mixtures, combustion rather than deflagration occurs at the top of the tube, the pressure of the high-temperature gas rises lowly, and the pressure history does not appear at the shock wave character. The fuel-riched products move into the divergent section of the tube and are re-ignited to induce strong detonation.
2007, 27(6): 493-500.
doi: 10.11883/1001-1455(2007)06-0493-08
Abstract:
The problem of asymmetric jet formation during the two-flow collision is theoretically unsolved yet, owing to steady solutions indeterminacy. Starting with special jets, we analyze the asymmetry between initial configuration of two incoming streams and their interaction. Based on principle of minimum kinetic energy, the close condition of equations is built, which is satisfied with the problem of asymmetric collision. The geometrical theory of asymmetric jet formation is given. Taking the collision of planar incoming streams with unequal thickness for example, we predict outgoing streams direction and size as a function of initial configuration of the incoming streams, which are in agreement with numerical results.
The problem of asymmetric jet formation during the two-flow collision is theoretically unsolved yet, owing to steady solutions indeterminacy. Starting with special jets, we analyze the asymmetry between initial configuration of two incoming streams and their interaction. Based on principle of minimum kinetic energy, the close condition of equations is built, which is satisfied with the problem of asymmetric collision. The geometrical theory of asymmetric jet formation is given. Taking the collision of planar incoming streams with unequal thickness for example, we predict outgoing streams direction and size as a function of initial configuration of the incoming streams, which are in agreement with numerical results.
2007, 27(6): 501-508.
doi: 10.11883/1001-1455(2007)06-0501-08
Abstract:
A generalized extension for the close condition of equations, which is satisfied with asymmetrical jet formation problem, is developed from head-on collision to asymmetrical oblique collision between two incoming streams. The geometrical theory of 2D planar asymmetric jet formation is presented. The critical condition and theoretical formula are obtained, which describe the formation of asymmetric jet. Variations of the width and direction of outgoing flows with collision anlge and initial configuration are theoretically predicted and numerically simulated under oblique collision. Theoretical results are in agreement with numerical results.
A generalized extension for the close condition of equations, which is satisfied with asymmetrical jet formation problem, is developed from head-on collision to asymmetrical oblique collision between two incoming streams. The geometrical theory of 2D planar asymmetric jet formation is presented. The critical condition and theoretical formula are obtained, which describe the formation of asymmetric jet. Variations of the width and direction of outgoing flows with collision anlge and initial configuration are theoretically predicted and numerically simulated under oblique collision. Theoretical results are in agreement with numerical results.
2007, 27(6): 509-514.
doi: 10.11883/1001-1455(2007)06-0509-06
Abstract:
The dynamic pre-buckling of finite cylindrical shells was discussed under both axial impact and internal or external pressure. A Hamiltonian system was constructed for the fundamental problem of the dynamic buckling, thereby problems of critical loads and buckling modes were reduced to determinations of eigenvalues and eigensolutions in a symplectic space and a symplectic method was proposed. Modes of the non-axisymmetric buckling were obtained by the proposed method. Numerical results show the critical loads, buckling modes and some phenomena for cylindrical shells.
The dynamic pre-buckling of finite cylindrical shells was discussed under both axial impact and internal or external pressure. A Hamiltonian system was constructed for the fundamental problem of the dynamic buckling, thereby problems of critical loads and buckling modes were reduced to determinations of eigenvalues and eigensolutions in a symplectic space and a symplectic method was proposed. Modes of the non-axisymmetric buckling were obtained by the proposed method. Numerical results show the critical loads, buckling modes and some phenomena for cylindrical shells.
2007, 27(6): 515-521.
doi: 10.11883/1001-1455(2007)06-0515-07
Abstract:
By using a splitting technique, the flux of the Navier Stokes governing equations including heat exchange and viscosity are divided into three parts, so called inviscid flux, viscous flux and heat flux, to calculate. The inviscid part of flux is evaluated using a high resolution multi-fluid parabolic piecewise method, the viscous part of flux is computed with a second order central difference in space and two-step Rung-Kutta scheme in time, and the heat flux part is not considered. Influences of fluid viscosity on instability of the interface between two fluids are revealed by computation results of the examples of Riemann problem in shock tube, two and three dimensional Richtmyer-Meshkov instabilities using the Navier Stokes governing equations and Euler governing equations.
By using a splitting technique, the flux of the Navier Stokes governing equations including heat exchange and viscosity are divided into three parts, so called inviscid flux, viscous flux and heat flux, to calculate. The inviscid part of flux is evaluated using a high resolution multi-fluid parabolic piecewise method, the viscous part of flux is computed with a second order central difference in space and two-step Rung-Kutta scheme in time, and the heat flux part is not considered. Influences of fluid viscosity on instability of the interface between two fluids are revealed by computation results of the examples of Riemann problem in shock tube, two and three dimensional Richtmyer-Meshkov instabilities using the Navier Stokes governing equations and Euler governing equations.
2007, 27(6): 522-528.
doi: 10.11883/1001-1455(2007)06-0522-07
Abstract:
This paper gives a brief description of smoothed particle hydrodynamics (SPH) method. By taking the advantages of SPH and standard finite element methods, a coupled method is proposed, in which the computational model is made up of finite elements in initial time and the large distortional elements are converted automatically into smoothed particles. Numerical examples for hypervelocity impact by the coupled method show that the coupled method is a more efficient method to simulation of large deformation problems in impact dynamics.
This paper gives a brief description of smoothed particle hydrodynamics (SPH) method. By taking the advantages of SPH and standard finite element methods, a coupled method is proposed, in which the computational model is made up of finite elements in initial time and the large distortional elements are converted automatically into smoothed particles. Numerical examples for hypervelocity impact by the coupled method show that the coupled method is a more efficient method to simulation of large deformation problems in impact dynamics.
2007, 27(6): 529-534.
doi: 10.11883/1001-1455(2007)06-0529-06
Abstract:
Dynamic and static resistances as well as resistance of steel bar to projectile when projectile colliding with steel bar are taken into consideration in the proposed engineering analytical model. Penetration depth and displacement, deceleration, velocity histories of projectiles with different impact velocities during penetration are calculated by using the proposed engineering analytical model and these calculated results are in good agreement with the experimental results. The peak rigid-body accelerations are between -12 000 g and -15 000 g (acceleration of gravity). The proposed model can represent the movement states of a projectile during its penetrating a semi-infinite reinforced concrete target, and it can be used to analyze the effect of configuration, size and mesh size of a steel bar on penetration depth and process.
Dynamic and static resistances as well as resistance of steel bar to projectile when projectile colliding with steel bar are taken into consideration in the proposed engineering analytical model. Penetration depth and displacement, deceleration, velocity histories of projectiles with different impact velocities during penetration are calculated by using the proposed engineering analytical model and these calculated results are in good agreement with the experimental results. The peak rigid-body accelerations are between -12 000 g and -15 000 g (acceleration of gravity). The proposed model can represent the movement states of a projectile during its penetrating a semi-infinite reinforced concrete target, and it can be used to analyze the effect of configuration, size and mesh size of a steel bar on penetration depth and process.
2007, 27(6): 535-540.
doi: 10.11883/1001-1455(2007)06-0535-06
Abstract:
Numerical simulation of the flow field of multi-cycle pulse detonation engine (PDE) is helpful for understanding the engine principle and performance analysis, and can provide the useful information for PDE design. The reactive Euler equations and a 9-species, 20-elementary-reactions model for hydrogen-air combustion were used to simulate the flow field of the first six cycles for a simplified two-dimensional PDE with a convergent-divergent nozzle. Results show that there are many distinctions between the single cycle and final steady flow fields. It needs five cycles until the flow fields reach the steady state, and the nozzle plays an important role in the engine internal flow.
Numerical simulation of the flow field of multi-cycle pulse detonation engine (PDE) is helpful for understanding the engine principle and performance analysis, and can provide the useful information for PDE design. The reactive Euler equations and a 9-species, 20-elementary-reactions model for hydrogen-air combustion were used to simulate the flow field of the first six cycles for a simplified two-dimensional PDE with a convergent-divergent nozzle. Results show that there are many distinctions between the single cycle and final steady flow fields. It needs five cycles until the flow fields reach the steady state, and the nozzle plays an important role in the engine internal flow.
2007, 27(6): 541-545.
doi: 10.11883/1001-1455(2007)06-0541-05
Abstract:
Dynamic compressive behaviors of carbon cloth /carbon composites were experimentally studied at the strain rates of 500, 1 500 s-1 by the split Hopkinson pressure bar with pulse shaper. Experimental results show that the pulse shaping technique ensures nearly constant strain-rate deformation experienced by specimens under dynamically equilibrated stresses so that accurate stress-strain curves at two high rates can be obtained. Compared with quasi-static compression, the dynamic compressive strength of carbon cloth/carbon composite has strong stain-rate sensitivity and it increases with strain rate. A phenomenological strain-rate-dependent material model of Cowper-Symonds power function was proposed to describe the stress-strain response of composites. The calculated results by the proposed model agree well with the experimental data at high and low strain rates.
Dynamic compressive behaviors of carbon cloth /carbon composites were experimentally studied at the strain rates of 500, 1 500 s-1 by the split Hopkinson pressure bar with pulse shaper. Experimental results show that the pulse shaping technique ensures nearly constant strain-rate deformation experienced by specimens under dynamically equilibrated stresses so that accurate stress-strain curves at two high rates can be obtained. Compared with quasi-static compression, the dynamic compressive strength of carbon cloth/carbon composite has strong stain-rate sensitivity and it increases with strain rate. A phenomenological strain-rate-dependent material model of Cowper-Symonds power function was proposed to describe the stress-strain response of composites. The calculated results by the proposed model agree well with the experimental data at high and low strain rates.
2007, 27(6): 546-552.
doi: 10.11883/1001-1455(2007)06-0546-07
Abstract:
Based on the equations for the conservation of mass, momentum, and energy together with the theory of plane shock wave and thermodynamics, a debris cloud model was proposed to characterize the debris cloud produced by normal impact of spherical projectile on thin plate shield. Characteristics of debris cloud calculated by using the proposed model are in agreement with the experimental results. Under different conditions, calculated results of characteristics for debris cloud by using the proposed model show the following conclusions. (1) The center-of-mass and spread velocities of debris cloud increase with the increase of impact velocity and projectile diameter, and decrease with the increase of shield thickness, and spread half angle increases with the increase of impact velocity and shield thickness and decreases with the increase of projectile diameter. (2)The change curves of velocity and spread half angle of debris cloud have similarities. (3)Under the determination of projectile and shield material, percentage by mass of materials in different phase states has relation only to impact velocity of projectile for the debris cloud loaded by shock wave. These conclusions are consistent with the experimental results.
Based on the equations for the conservation of mass, momentum, and energy together with the theory of plane shock wave and thermodynamics, a debris cloud model was proposed to characterize the debris cloud produced by normal impact of spherical projectile on thin plate shield. Characteristics of debris cloud calculated by using the proposed model are in agreement with the experimental results. Under different conditions, calculated results of characteristics for debris cloud by using the proposed model show the following conclusions. (1) The center-of-mass and spread velocities of debris cloud increase with the increase of impact velocity and projectile diameter, and decrease with the increase of shield thickness, and spread half angle increases with the increase of impact velocity and shield thickness and decreases with the increase of projectile diameter. (2)The change curves of velocity and spread half angle of debris cloud have similarities. (3)Under the determination of projectile and shield material, percentage by mass of materials in different phase states has relation only to impact velocity of projectile for the debris cloud loaded by shock wave. These conclusions are consistent with the experimental results.
Study on theory and method of reliability assessment of explosive initiator based on testing entropy
2007, 27(6): 553-556.
doi: 10.11883/1001-1455(2007)06-0553-04
Abstract:
To decrease testing samples and avoid the risk caused by estimated error of scale factor , a new statistical method was introduced in the tests on reliability assessment of explosive initiator. The concept of entropy was presented and the equation of testing entropy equivalence was given. This testing entropy equivalence method for assessing reliability of explosive initiator was put forward according to the distribution function of sensitivity and application of go/no-go and sequential methods together. The feasibility and correctness were validated in the control tests of detonator reliability assessment with large samples compared with small samples. Results show that reliability of explosive initiator with high index can be assessed in small samples.
To decrease testing samples and avoid the risk caused by estimated error of scale factor , a new statistical method was introduced in the tests on reliability assessment of explosive initiator. The concept of entropy was presented and the equation of testing entropy equivalence was given. This testing entropy equivalence method for assessing reliability of explosive initiator was put forward according to the distribution function of sensitivity and application of go/no-go and sequential methods together. The feasibility and correctness were validated in the control tests of detonator reliability assessment with large samples compared with small samples. Results show that reliability of explosive initiator with high index can be assessed in small samples.
2007, 27(6): 557-561.
doi: 10.11883/1001-1455(2007)06-0557-05
Abstract:
Considering the quantum-mechanical effect at lower temperatures, the modified Weeks-Chandler-Andersen theory and improved variational perturbation principle were used to develop the single and double shock dynamic equations of state of liquid helium at the pressures ranging from 0 to 108 GPa and the temperatures ranging from 471 to 32 790 K. The appropriate exp-6 potential parameters were obtained by fitting the experimental data based on determined interactions of molecules in liquid helium. The calculated results are in good agreement with the experimental data.
Considering the quantum-mechanical effect at lower temperatures, the modified Weeks-Chandler-Andersen theory and improved variational perturbation principle were used to develop the single and double shock dynamic equations of state of liquid helium at the pressures ranging from 0 to 108 GPa and the temperatures ranging from 471 to 32 790 K. The appropriate exp-6 potential parameters were obtained by fitting the experimental data based on determined interactions of molecules in liquid helium. The calculated results are in good agreement with the experimental data.
2007, 27(6): 562-566.
doi: 10.11883/1001-1455(2007)06-0562-05
Abstract:
By adopting wedge-shaped charge and using critical thickness to characterize detonation waves propagation, a experimental study was carried out to explore influences of particle size of HMX on detonation waves propagation of HMX and HMX/F2641 at the two different densities of HMX. Experimental results show as follows: (1) Decrease in size of HMX particle results in diminution of critical thickness, namely enhancement of detonation wave propagation capability; (2) HMX/F2641excels HMX in detonation wave propagation capability at the same size of HMX particle; (3) Increase of charge density is advantageous to detonation waves propagation.
By adopting wedge-shaped charge and using critical thickness to characterize detonation waves propagation, a experimental study was carried out to explore influences of particle size of HMX on detonation waves propagation of HMX and HMX/F2641 at the two different densities of HMX. Experimental results show as follows: (1) Decrease in size of HMX particle results in diminution of critical thickness, namely enhancement of detonation wave propagation capability; (2) HMX/F2641excels HMX in detonation wave propagation capability at the same size of HMX particle; (3) Increase of charge density is advantageous to detonation waves propagation.
2007, 27(6): 567-571.
doi: 10.11883/1001-1455(2007)06-0567-05
Abstract:
Deflagration-to-detonation transition (DDT) of composition B (TNT/RDX=40/60) with density 1.597 g/cm3 is experimentally explored by using the electrical pin and pressure sensor measurement techniques. Experimental results show that a DDT is obtained under the strong confinement condition (steel tube with inner diameter 20 mm and outer diameter 64 mm and length 500 mm), and that the detonation-induced distance is 295 ~310 mm.
Deflagration-to-detonation transition (DDT) of composition B (TNT/RDX=40/60) with density 1.597 g/cm3 is experimentally explored by using the electrical pin and pressure sensor measurement techniques. Experimental results show that a DDT is obtained under the strong confinement condition (steel tube with inner diameter 20 mm and outer diameter 64 mm and length 500 mm), and that the detonation-induced distance is 295 ~310 mm.
2007, 27(6): 572-576.
doi: 10.11883/1001-1455(2007)06-0572-05
Abstract:
Base on aerodynamics and related rocket engine theories, two types of dual-rail sleds were designed and experimentally tested on a 600 m long non-gap sled rail. Velocities of sled were measured by using the three methods of magnetic induction, laser interferometry and high-speed photography respectively. Their speeds reached 45 m/s under 50 kg load and 200 m/s under 100 kg load respectively. Experimental results indicate that the velocities obtained by the three test techniques are consistent with each other and the measured velocities are in good agreement with the calculated results.
Base on aerodynamics and related rocket engine theories, two types of dual-rail sleds were designed and experimentally tested on a 600 m long non-gap sled rail. Velocities of sled were measured by using the three methods of magnetic induction, laser interferometry and high-speed photography respectively. Their speeds reached 45 m/s under 50 kg load and 200 m/s under 100 kg load respectively. Experimental results indicate that the velocities obtained by the three test techniques are consistent with each other and the measured velocities are in good agreement with the calculated results.
